Question

1. 82, 23, 59, 94, 70, 26, 32, 83, 87, 94, 32

mean ___ median _ mode ________ range __

Explanation:

Step1: Calculate the Mean

First, sum all the numbers: \(82 + 23 + 59 + 94 + 70 + 26 + 32 + 83 + 87 + 94 + 32\)
\(= (82+23)+(59+94)+(70+26)+(32+83)+(87+94)+32\)
\(= 105 + 153 + 96 + 115 + 181 + 32\)
\(= (105+153)+(96+115)+(181+32)\)
\(= 258 + 211 + 213\)
\(= 258+424 = 682\)
There are 11 numbers, so the mean is \(\frac{682}{11} = 62\).

Step2: Calculate the Median

First, sort the numbers in ascending order: \(23, 26, 32, 32, 59, 70, 82, 83, 87, 94, 94\)
There are 11 numbers (odd count), so the median is the 6th number, which is \(70\).

Step3: Calculate the Mode

The mode is the number that appears most frequently. Here, \(32\) and \(94\) both appear twice, more than any other number. So modes are \(32\) and \(94\).

Step4: Calculate the Range

The range is the maximum number minus the minimum number. Max is \(94\), min is \(23\), so range is \(94 - 23 = 71\).

Answer:

Mean: \(62\), Median: \(70\), Mode: \(32, 94\), Range: \(71\)