Question

the table gives the heights, in centimeters, of a group of sixth graders.
140 152 135 158 160 144 129 150 155
place the values to show the median height and the range of heights, in centimeters, for this set of data.
median height =
range =
:: 15 :: 21 :: 31
:: 129 :: 150 :: 160

Explanation:

Step1: Order the data

First, we order the heights from least to greatest: \(129, 135, 140, 144, 150, 152, 155, 158, 160\) (wait, wait, original data: 140, 152, 135, 158, 160, 144, 129, 150, 155. Let's count the number of data points: 9 values. So ordering: 129, 135, 140, 144, 150, 152, 155, 158, 160.

Step2: Find the median

For a set with \(n = 9\) (odd number of values), the median is the \(\frac{n + 1}{2}\)-th term. \(\frac{9+1}{2}=5\)-th term. The 5th term in the ordered list is 150. So median height is 150.

Step3: Find the range

Range is maximum value minus minimum value. Maximum value is 160, minimum is 129. So range \(= 160 - 129 = 31\)? Wait, no: 160 - 129 = 31? Wait 160 - 129: 160 - 130 = 30, plus 1 is 31. Wait but the options have 21, 31, 15. Wait maybe I miscalculated. Wait original data: 129, 135, 140, 144, 150, 152, 155, 158, 160. Max is 160, min is 129. 160 - 129 = 31. Wait but the options have 31 as a tile. And median is 150 (since 5th term is 150). Let's check again.

Wait the data points: 140, 152, 135, 158, 160, 144, 129, 150, 155. Let's list them in order: 129, 135, 140, 144, 150, 152, 155, 158, 160. Number of terms: 9. So median is the 5th term, which is 150. Range: 160 - 129 = 31. Wait but the tiles have 15, 21, 31, 129, 150, 160. Wait 160 - 129 is 31, so range is 31. Median is 150.

Answer:

Median Height = 150
Range = 31