Step-by-step explanation:
The five number summary includes the mean, the median, the mode, the range, and the interquartile range.
1) Mean = The sum of all observations / number of observations.
Mean = (21 + 22 + 22 + 24 + 24 + 24 + 24 + 25 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 26 + 27 + 27 + 27 + 27 + 28 + 28 + 28 + 28 + 29 + 29 + 29 + 29 + 29 + 30 + 30 + 30 + 30 + 30 + 30 + 31 + 31 + 31 + 32 + 32 + 33 + 33 + 33 + 33 + 33 + 33 + 33 + 34 + 34 + 34 + 34 + 34 + 35 + 35 + 35 + 35 + 35 + 37 + 37 + 37 + 37 + 38 + 38 + 38 + 39 + 39 + 39 + 41 + 41 + 41 + 41 + 42 + 42 + 44 + 45 + 45 + 45 + 47 + 49 + 49 + 54 + 60 + 60 + 61 + 61 + 61 + 62 + 62 + 74 + 81)/91.
Mean = 3285/91
Mean = 36 (round to the nearest whole number).
2) Median = The central point of the data.
91 divided by 2 gives 45.5, which means 45th number will be the median of this data set. So, Median = 33.
3) Mode = The mostly repeated observation of the data.
Mode = 26 (repeated 9 times).
4) Range = Largest observation - Smallest observation
Range = 81 - 21 = 60.
5) Interquartile Range = Upper Quartile - Lower Quartile.
Upper Quartile is the data point at the 75% position of the data.
Lower Quartile is the data point at the 25% position of the data.
Upper Quartile position = 91*0.75 = 68.25 (68th position).
So that observation is 39.
Lower Quartile position = 91*0.25 = 22.75 (22nd position).
So that observation is 28.
Therefore, interquartile range = 39 - 28 = 11!!!
