Question

The weights in pounds, of a group of students are as follows
173 123 171 175 188 120 177 160 151 169
162 128 145 140 158 132 202 162 154 180
164 166 157 171 175
Find the five-number summary for the data. Which boxplot best represents the data?
a
100 110 120 130 140 150 160 170 180 190 200 210
b
100 110 120 130 140 150 160 170 180 190 200 210
C
+ +
100 110 120 130 140 150 160 170 180 190 200 210
d.
100 110 120 130 140 150 160 170 180 190 200 210

Answer 1

Mean: 160.12

Standard Deviation: 19.76

Median: 162

Maximum: 202

Minimum: 120

The mean is calculated by adding all of the numbers in the data set and dividing by the number of values that were added:

173 + 123 + 171 + 175 + 188 + 120 + 177 + 160  + 151 + 169 + 162 + 128 + 145 + 140 + 158 + 132 + 202 + 162 + 154 + 180 + 164 + 166 + 157 + 171 + 175 ÷ 25 = 160.12

Standard deviation is found by calculating the mean (160.12) , and then subtracting the mean and square root result for each number. Finally, working out the mean of the squared differences and taking the square root of the final answer results in a standard deviation of 19.76. (The attached image has the formula for finding standard deviation).

Median is the number that is found in the middle when placing the numbers in order from least to greatest.

The maximum is the largest number in the data set.

The minimum is the smallest number in the data set.