Question

Sanjay tried to find the median from the following dot plot, which shows how far he went on his recent walks. however, he made a mistake. [5] [6] [7] [8] [9] here is sanjay's work: "the numbers are [5], [6], [6], [7], [8], [8], [9], and [9]. there are [8] values, so the middle value is the 4th value, [7]. the median is [7] kilometers." what mistake did sanjay make? Choose 1 answer:

a) Sanjay calculated the mean instead of the median.
b) Sanjay should have ordered the numbers from least to greatest before picking the middle number.
c) Sanjay should have averaged the middle [2] values instead of using just [1] value.
d) Sanjay shouldn't have repeated any of the values in his list.

Answer 1

Sanjay's mistake was that he did not average the middle two values to find the median, since the set contains an even number of values.

Step-by-step explanation:

Sanjay made a mistake by not correctly calculating the median from the given data set. Since there are eight values in the set, and eight is an even number, the median should be found by averaging the middle two values. These are the 4th and the 5th values when listed in order. Sanjay incorrectly chose the 4th value as the median without averaging it with the 5th value.

The correct calculation for the median is to take the mean of the 4th and 5th value. In Sanjay's case, the 4th value is [7] and the 5th value is [8]. Therefore, the median is (7 + 8) / 2 which equals 7.5 kilometers.