#### 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
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.