Mathbench

11. Descriptive statistics

Mean, median and the spread of a data set. Set for OMPT-E.

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Questions

Sheet length
1

For the data set 2,16,8,28,23,172, 16, 8, 28, 23, 17, give the exact MEDIAN.

Answer:

2

For the data set 22,16,26,5,422, 16, 26, 5, 4, give the exact VARIANCE.

Answer:

3

For the data set 11,13,30,10,1,16,1811, 13, 30, 10, 1, 16, 18, give the exact MEAN.

Answer:

4

For the data set 16,21,11,28,2416, 21, 11, 28, 24, give the exact VARIANCE.

Answer:

5

For the data set 11,16,7,12,13,1111, 16, 7, 12, 13, 11, give the exact MEAN.

Answer:

6

For the data set 18,25,17,18,2918, 25, 17, 18, 29, give the exact VARIANCE.

Answer:

7

For the data set 5,28,30,28,295, 28, 30, 28, 29, give the exact MEDIAN.

Answer:

8

For the data set 21,6,8,21,2621, 6, 8, 21, 26, give the exact RANGE.

Answer:

9

For the data set 24,7,19,11,26,19,1224, 7, 19, 11, 26, 19, 12, give the exact MEAN.

Answer:

10

For the data set 27,23,10,24,1427, 23, 10, 24, 14, give the exact VARIANCE.

Answer:

11

For the data set 26,7,17,16,14,2426, 7, 17, 16, 14, 24, give the exact MEDIAN.

Answer:

12

For the data set 2,5,28,12,162, 5, 28, 12, 16, give the exact VARIANCE.

Answer:

13

For the data set 18,21,20,4,1818, 21, 20, 4, 18, give the exact MEDIAN.

Answer:

14

For the data set 18,28,20,19,518, 28, 20, 19, 5, give the exact VARIANCE.

Answer:

15

For the data set 10,2,24,19,29,2810, 2, 24, 19, 29, 28, give the exact MEAN.

Answer:

16

For the data set 23,13,26,15,1023, 13, 26, 15, 10, give the exact RANGE.

Answer:

17

For the data set 21,2,9,12,25,1421, 2, 9, 12, 25, 14, give the exact MEAN.

Answer:

18

For the data set 4,17,15,1,94, 17, 15, 1, 9, give the exact RANGE.

Answer:

19

For the data set 18,16,5,10,9,2318, 16, 5, 10, 9, 23, give the exact MEAN.

Answer:

20

For the data set 27,1,1,8,227, 1, 1, 8, 2, give the exact VARIANCE.

Answer:

21

For the data set 8,7,2,4,1,18,108, 7, 2, 4, 1, 18, 10, give the exact MEAN.

Answer:

22

For the data set 23,24,14,7,2523, 24, 14, 7, 25, give the exact VARIANCE.

Answer:

23

For the data set 29,11,14,27,1,1229, 11, 14, 27, 1, 12, give the exact MEDIAN.

Answer:

24

For the data set 4,14,9,4,274, 14, 9, 4, 27, give the exact RANGE.

Answer:

25

For the data set 24,4,6,4,11,7,1624, 4, 6, 4, 11, 7, 16, give the exact MEDIAN.

Answer:

26

For the data set 27,4,9,8,227, 4, 9, 8, 2, give the exact VARIANCE.

Answer:

27

For the data set 2,3,18,22,14,242, 3, 18, 22, 14, 24, give the exact MEDIAN.

Answer:

28

For the data set 1,27,11,11,41, 27, 11, 11, 4, give the exact RANGE.

Answer:

29

For the data set 8,4,29,2,1,108, 4, 29, 2, 1, 10, give the exact MEAN.

Answer:

30

For the data set 16,3,28,26,2616, 3, 28, 26, 26, give the exact VARIANCE.

Answer:

Answers

Every answer below was re-derived independently before this page was built.

1

Answer: 332\frac{33}{2}

Put the values in order first — 2,8,16,17,23,282, 8, 16, 17, 23, 28 — then take the middle one: 332\frac{33}{2}.

Common mistakes, and the answer each one gives:

  • Gave the mean instead of the median → 473\frac{47}{3}
  • Took the middle of the list AS WRITTEN, without sorting it first → 2828
2

Answer: 195625\frac{1956}{25}

The mean is 735\frac{73}{5}. Square each value's distance from it, add those up and divide by 55: 195625\frac{1956}{25}.

Common mistakes, and the answer each one gives:

  • Gave the range instead of the variance → 2222
  • Added the distances from the mean without squaring them → 20225\frac{202}{25}
3

Answer: 997\frac{99}{7}

The mean is the total divided by how many there are: 997=997\dfrac{99}{7} = \frac{99}{7}.

Common mistakes, and the answer each one gives:

  • Gave the median instead of the mean → 1313
  • Took the middle of the list AS WRITTEN, without sorting it first → 1010
4

Answer: 1785\frac{178}{5}

The mean is 2020. Square each value's distance from it, add those up and divide by 55: 1785\frac{178}{5}.

Common mistakes, and the answer each one gives:

  • Gave the range instead of the variance → 1717
  • Added the distances from the mean without squaring them → 265\frac{26}{5}
5

Answer: 353\frac{35}{3}

The mean is the total divided by how many there are: 706=353\dfrac{70}{6} = \frac{35}{3}.

Common mistakes, and the answer each one gives:

  • Gave the median instead of the mean → 232\frac{23}{2}
  • Took the middle of the list AS WRITTEN, without sorting it first → 1212
6

Answer: 56625\frac{566}{25}

The mean is 1075\frac{107}{5}. Square each value's distance from it, add those up and divide by 55: 56625\frac{566}{25}.

Common mistakes, and the answer each one gives:

  • Gave the range instead of the variance → 1212
  • Added the distances from the mean without squaring them → 11225\frac{112}{25}
7

Answer: 2828

Put the values in order first — 5,28,28,29,305, 28, 28, 29, 30 — then take the middle one: 2828.

Common mistakes, and the answer each one gives:

  • Gave the mean instead of the median → 2424
  • Took the middle of the list AS WRITTEN, without sorting it first → 3030
8

Answer: 2020

The range is the largest value minus the smallest: 26−6=2026 - 6 = 20.

Common mistakes, and the answer each one gives:

  • Gave the variance instead of the range → 156625\frac{1566}{25}
  • Added the distances from the mean without squaring them → 18825\frac{188}{25}
9

Answer: 1187\frac{118}{7}

The mean is the total divided by how many there are: 1187=1187\dfrac{118}{7} = \frac{118}{7}.

Common mistakes, and the answer each one gives:

  • Gave the median instead of the mean → 1919
  • Took the middle of the list AS WRITTEN, without sorting it first → 1111
10

Answer: 104625\frac{1046}{25}

The mean is 985\frac{98}{5}. Square each value's distance from it, add those up and divide by 55: 104625\frac{1046}{25}.

Common mistakes, and the answer each one gives:

  • Gave the range instead of the variance → 1717
  • Added the distances from the mean without squaring them → 15225\frac{152}{25}
11

Answer: 332\frac{33}{2}

Put the values in order first — 7,14,16,17,24,267, 14, 16, 17, 24, 26 — then take the middle one: 332\frac{33}{2}.

Common mistakes, and the answer each one gives:

  • Gave the mean instead of the median → 523\frac{52}{3}
  • Took the middle of the list AS WRITTEN, without sorting it first → 1616
12

Answer: 209625\frac{2096}{25}

The mean is 635\frac{63}{5}. Square each value's distance from it, add those up and divide by 55: 209625\frac{2096}{25}.

Common mistakes, and the answer each one gives:

  • Gave the range instead of the variance → 2626
  • Added the distances from the mean without squaring them → 18825\frac{188}{25}
13

Answer: 1818

Put the values in order first — 4,18,18,20,214, 18, 18, 20, 21 — then take the middle one: 1818.

Common mistakes, and the answer each one gives:

  • Gave the mean instead of the median → 815\frac{81}{5}
  • Took the middle of the list AS WRITTEN, without sorting it first → 2020
14

Answer: 2745\frac{274}{5}

The mean is 1818. Square each value's distance from it, add those up and divide by 55: 2745\frac{274}{5}.

Common mistakes, and the answer each one gives:

  • Gave the range instead of the variance → 2323
  • Added the distances from the mean without squaring them → 265\frac{26}{5}
15

Answer: 563\frac{56}{3}

The mean is the total divided by how many there are: 1126=563\dfrac{112}{6} = \frac{56}{3}.

Common mistakes, and the answer each one gives:

  • Gave the median instead of the mean → 432\frac{43}{2}
  • Took the middle of the list AS WRITTEN, without sorting it first → 1919
16

Answer: 1616

The range is the largest value minus the smallest: 26−10=1626 - 10 = 16.

Common mistakes, and the answer each one gives:

  • Gave the variance instead of the range → 92625\frac{926}{25}
  • Added the distances from the mean without squaring them → 14225\frac{142}{25}
17

Answer: 836\frac{83}{6}

The mean is the total divided by how many there are: 836=836\dfrac{83}{6} = \frac{83}{6}.

Common mistakes, and the answer each one gives:

  • Gave the median instead of the mean → 1313
  • Took the middle of the list AS WRITTEN, without sorting it first → 1212
18

Answer: 1616

The range is the largest value minus the smallest: 17−1=1617 - 1 = 16.

Common mistakes, and the answer each one gives:

  • Gave the variance instead of the range → 94425\frac{944}{25}
  • Added the distances from the mean without squaring them → 13625\frac{136}{25}
19

Answer: 272\frac{27}{2}

The mean is the total divided by how many there are: 816=272\dfrac{81}{6} = \frac{27}{2}.

Common mistakes, and the answer each one gives:

  • Gave the median instead of the mean → 1313
  • Took the middle of the list AS WRITTEN, without sorting it first → 1010
20

Answer: 247425\frac{2474}{25}

The mean is 395\frac{39}{5}. Square each value's distance from it, add those up and divide by 55: 247425\frac{2474}{25}.

Common mistakes, and the answer each one gives:

  • Gave the range instead of the variance → 2626
  • Added the distances from the mean without squaring them → 19425\frac{194}{25}
21

Answer: 507\frac{50}{7}

The mean is the total divided by how many there are: 507=507\dfrac{50}{7} = \frac{50}{7}.

Common mistakes, and the answer each one gives:

  • Gave the median instead of the mean → 77
  • Took the middle of the list AS WRITTEN, without sorting it first → 44
22

Answer: 122625\frac{1226}{25}

The mean is 935\frac{93}{5}. Square each value's distance from it, add those up and divide by 55: 122625\frac{1226}{25}.

Common mistakes, and the answer each one gives:

  • Gave the range instead of the variance → 1818
  • Added the distances from the mean without squaring them → 16225\frac{162}{25}
23

Answer: 1313

Put the values in order first — 1,11,12,14,27,291, 11, 12, 14, 27, 29 — then take the middle one: 1313.

Common mistakes, and the answer each one gives:

  • Gave the mean instead of the median → 473\frac{47}{3}
  • Took the middle of the list AS WRITTEN, without sorting it first → 2727
24

Answer: 2323

The range is the largest value minus the smallest: 27−4=2327 - 4 = 23.

Common mistakes, and the answer each one gives:

  • Gave the variance instead of the range → 182625\frac{1826}{25}
  • Added the distances from the mean without squaring them → 17825\frac{178}{25}
25

Answer: 77

Put the values in order first — 4,4,6,7,11,16,244, 4, 6, 7, 11, 16, 24 — then take the middle one: 77.

Common mistakes, and the answer each one gives:

  • Gave the mean instead of the median → 727\frac{72}{7}
  • Took the middle of the list AS WRITTEN, without sorting it first → 44
26

Answer: 3945\frac{394}{5}

The mean is 1010. Square each value's distance from it, add those up and divide by 55: 3945\frac{394}{5}.

Common mistakes, and the answer each one gives:

  • Gave the range instead of the variance → 2525
  • Added the distances from the mean without squaring them → 345\frac{34}{5}
27

Answer: 1616

Put the values in order first — 2,3,14,18,22,242, 3, 14, 18, 22, 24 — then take the middle one: 1616.

Common mistakes, and the answer each one gives:

  • Gave the mean instead of the median → 836\frac{83}{6}
  • Took the middle of the list AS WRITTEN, without sorting it first → 2222
28

Answer: 2626

The range is the largest value minus the smallest: 27−1=2627 - 1 = 26.

Common mistakes, and the answer each one gives:

  • Gave the variance instead of the range → 202425\frac{2024}{25}
  • Added the distances from the mean without squaring them → 16625\frac{166}{25}
29

Answer: 99

The mean is the total divided by how many there are: 546=9\dfrac{54}{6} = 9.

Common mistakes, and the answer each one gives:

  • Gave the median instead of the mean → 66
  • Took the middle of the list AS WRITTEN, without sorting it first → 22
30

Answer: 220425\frac{2204}{25}

The mean is 995\frac{99}{5}. Square each value's distance from it, add those up and divide by 55: 220425\frac{2204}{25}.

Common mistakes, and the answer each one gives:

  • Gave the range instead of the variance → 2525
  • Added the distances from the mean without squaring them → 20625\frac{206}{25}