The heights, in centimeters, of 10 students are given in the table. 160 159
158.5 168
162 164.5
164 169
161 160.5

Sam creates a box plot for this data. Match the values to the correct locations on the box plot.

161.5
158.5
160
164.5
159
169
168
162

Minimum Value = 158.5

First Quartile = 160

Median = 161.5

Third Quartile = 164.5

Maximum Value = 169

Step-by-step explanation:

The box plot consists of five number summary

Minimum Value, First Quartile, Median, Third Quartile and Maximum Value.

The given data is:

160,159, 158.5,168,162,164.5,164,169,161, 160.5

First arranging data in ascending order:

158.5,159,160,160.5,161,162,164,164.5,168,169

Now, finding values of five number summary

Minimum Value = 158.5

Maximum Value = 169

Median (average the middle two terms i.e 5th and 6th term) = (161+162)/2 = 161.5

First Quartile = 1/4(n+1) th term = 1/4(10+1) = 1/4(11) = 2.75 ≅ 3

So, first quartile is 3rd term: 160

Third Quartile = 3/4(n+1) = 3/4(10+1) = 3/4(11) = 8.25 ≅ 8

So, third quartile is 8th term i.e 164.5

Now, placing value in the figure in order of:

Minimum Value = 158.5

First Quartile = 160

Median = 161.5

Third Quartile = 164.5

Maximum Value = 169

Figure is also attached.