Grade 12 - More exercises.
Mean, median, mode and range.
1.
Calculate
the mean, median, mode and range of the following data sets.
1.1
18 ; 24 ; 19 ; 20 ; 28 ;
19 ; 26 ; 21 ; 22 ; 16 ; 17
1.2
17 ; 14 ; 11 ; 18 ; 16 ;
17 ; 21 ; 12 ; 22 ; 17
1.3
38 ; 60 ; 63 ; 57 ; 60 ;
58 ; 59
1.4
50 ; 52 ; 58 ; 51 ; 49 ;
51 ; 80 ; 53 ; 50
1.5
14 ; 38 ; 23 ; 18 ; 27 ;
30
1.6
19 ; 13 ; 23 ; 19 ; 21 ;
19 ; 19
1.7
4 ; 17 ; 15 ; 11 ; 25 ;
15 ; 7 ; 15 ; 11 ; 8
1.8
37 ; 31 ; 33 ; 34 ; 32 ;
37 ; 31 ; 30 ; 37
2.
Say which
of the following values, mean, median and mode, describe each of
the following
sets of data the best and give reasons:
2.1
36 ;
34 ; 31 ; 34 ; 37 ; 32
; 34
2.2
7 ;
8 ; 31 ; 6 ; 9 ; 7
; 8 ; 7 ; 6
2.3
15 ;
11 ; 3 ; 16 ; 16 ; 15
2.4
20 ;
17 ; 20 ; 18 ; 23 ; 20
2.5
22 ;
26 ; 22 ; 62 ; 21 ; 25
; 24 ; 22
2.6
51 ;
54 ; 92 ; 52 ; 48 ; 53
; 57 ; 13
3.
For
each set of data calculate the median, 1st, 2nd and 3rd quartiles, the inter quartile width,
the 20th,
25th, 75th and 80th percentiles. Also write down the boundaries
between which we find the
middle
50% of the data values. Write down the maximum value for the bottom 25% of the
values
and also the minimum for the top 20% of the values.
3.1
16 ;
33 ; 38 ; 3 ; 23 ; 35 ;
8 ; 15 ; 37 ; 24 ; 36 ;
21 ; 18 ; 31
3.2
48 ; 71 ; 58 ; 49 ; 75 ;
57 ; 96 ; 67 ; 92 ; 51 ;
63 ; 95 ; 72 ; 51 ; 93 ;
53 ; 54 ; 73 ; 55
3.3
9 ; 13 ; 42 ; 2 ; 44 ; 15 ;
13 ; 31 ; 18 ; 43 ; 3 ;
14 ; 23 ; 13 ; 5 ;
16 ; 4 ; 12 ; 41 ; 7 ; 25 ;
34 ; 11
3.4
40 ; 41 ; 31 ; 52 ; 44 ;
32 ; 41 ; 35 ; 49 ; 42 ;
34 ; 37 ; 36 ; 48 ;
41 ; 35
4.
A set of
data consists of 5 different values. The mean is 23,2 and the median is 24.
The
range is 10 and the greatest value is 28.
4.1
Calculate
the smallest value.
4.2
Write down the
value of the mode. Explain your answer.
4.3
How many
values are smaller than the median and how many are greater than the median? Explain.
4.4
How many
values are between the median and the greatest value? Explain.
4.5
Calculate
the approximate sum of all the data values.
5.
The mean
of 7 data values is 17,143 and the median is 17. The smallest value is
14, the range is 6 and the mode is 19.
5.1
Calculate the
greatest value of the set.
5.2
How many
values are smaller than 17 and how many are greater than 17? Explain.
5.3
Calculate
the approximate sum of the data set.
5.4
How many
values are there between 14 and 17?
5.5
How many
values are between 17 and 20? Can you write them down? Explain.
6.
A set of
data consists of 9 integer values. The smallest value is 7 and the
range is 26. The mean is 18, the median is 17 and the mode is 27.
6.1
Write down
the largest value.
6.2
How many
values are smaller than the median and how many are larger than the median? Explain.
6.3
How many
values are larger than the mean? Explain.
6.4
Write down
all the values greater than 16.
6.5
Calculate the
approximate sum of all the values.
6.6
Calculate
the sum of the values in 6.4
6.7
Calculate
the sum of al the values smaller than the median.
7.
A
data set contains 10 integer values. The median is 9, the mod is 8 (frequency of 2)
and the mean is 10,5. The smallest number is 2 and the range is 19.
7.1
Calculate the
biggest value.
7.2
How many
values are smaller than and how many are larger than the median? Explain.
7.3
Will it be
correct to claim that 50% of the values are smaller than 9? Explain.
7.4
How many
values are greater than the mean? Explain.
7.5
Calculate the
approximate sum of al the values.
7.6
How many
values are smaller than the mode? Explain.
8.
A batsman
scored an average of 23,1 runs in 7 matches. The runs scored in each of the
first 6
matches were: 21 ; 8 ; 6 ; 88 ; 3 ;
5
8.1
How many
runs did he score in the seventh match?
8.2
Is the average of his scores a good description of his scores? Explain.
The scores
of a second batsman were: 23 ; 18 ; 20 ; 21 ;
17 ; 19 ; 20
8.3
Calculate the average of his scores.
8.4
If you were
to select a steady batsman, would you choose the first or the second batsman? Explain.