Question

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QUESTION 1: Create a boxplot for the weights of the women.

QUESTION 2: Find the mean weight for men. Round to 3 decimal places.

QUESTION 3: Find the median weight for men.

QUESTION 4:Find the mode for the men's weights.

QUESTION 5: Find the midrange for the women's weights.

QUESTION 6: Find the standard deviation for the women's weights. Round to 3 decimal places.

QUESTION 7: Find the standard deviation for the men's weights. Round to 3 decimal places.

QUESTION 8: Find the range for the women's weights.

QUESTION 9: Find the range for the men's weights.

QUESTION 10: For the women's weights, find the score at the 80th percentile.

QUESTION 11: For the men's weights, find the score at the 80th percentile.

QUESTION 12: Would it be considered unusual for a female to weigh 120 pounds? Prove your answer by using the z-score.

Answer 1

Q1. To create box plot for weight of women , we need maximum weight, minimum weight , first quartile weight, third quartile weight and median, that is five number of summary.

Minimum Weight (in pounds) = 102 , Maximum weight (in pounds) = 161

Since data set has total data values for women = 15 , including median first half and second half of data set contains 8 values. so first quartile would be average of 4th and 5th values , and third quartile would be average of 11th and 12th values.   

Here is Female weight in ascending order with median , first quartile , second quartile weight.

Datavalue location Female 102 ام <----- First Quartile value = 4th and 5 locaiton value avg = (115+122)/2 = 118.5 اما یاد ہے 109 115 115 122 122 123 124 133 134 135 141 141 154 --- Median value = 124 172_ <--...-- Third Quartile Value = 11th and 12th location value avg| = (135 + 141)/2 = 138 15 161

Here is box plot.

BoxPlot 100 110 120 150 160 170 130 140 Female

Q2: Mean weight for men.

Datavalue location	Weight (Pounds)
1	144
2	149
3	155
4	157
5	158
6	159
7	166
8	166
9	166
10	168
11	178
12	194
13	194
14	198
15	205
16	206

Sample size = n = 16

$\text{mean weight} = \frac{\sum (Weight)}{n} = 2763 / 16 = 172.686$

Q3: Median weight for Male

Datavalue Weight location (Pounds) 1 144 2 149 155 157 158 159 166 166 <------ Median value = 8th and 9th location value avg = (166 + 166)/2 = 166 166 168 178 194 194) 198 205 206

As explained in above table , Median weight of male = 166 Pounds.

Q4. Find the mode for the Men weight.

As shown in Answer 3 , It is evident with above men weight that 166 pounds have maximum frequency of 3. Hence mode for Men weight = 166 pounds.