Question

1. 82, 45, 43, 52, 41, 66, 38, 67, 88, 59, 54

mean __ median mode ____ range __
if there is no mode put
one\
mean is
median is
mode is
range is

Explanation:

Step1: Sort the data

First, we sort the given data set: \(38, 41, 43, 45, 52, 54, 59, 65, 67, 82, 88\) (Wait, the original data has 11 numbers? Wait, let's check the original data: 82, 45, 43, 52, 41, 65, 38, 67, 88, 59, 54. Let's count: 11 numbers. So sorted: \(38, 41, 43, 45, 52, 54, 59, 65, 67, 82, 88\)

Step2: Calculate the Mean

The mean is the sum of all values divided by the number of values.
Sum = \(38 + 41 + 43 + 45 + 52 + 54 + 59 + 65 + 67 + 82 + 88\)
Let's calculate the sum:
\(38+41 = 79\); \(79+43 = 122\); \(122+45 = 167\); \(167+52 = 219\); \(219+54 = 273\); \(273+59 = 332\); \(332+65 = 397\); \(397+67 = 464\); \(464+82 = 546\); \(546+88 = 634\)
Number of values \(n = 11\)
Mean = \(\frac{634}{11} \approx 57.64\) (Wait, the given mean in the image is 127.6, which is wrong. Let's recalculate the sum correctly. Wait, maybe I misread the data. Let's check the original data again: 82, 45, 43, 52, 41, 65, 38, 67, 88, 59, 54. Let's add again:
38 + 41 = 79; 79 + 43 = 122; 122 + 45 = 167; 167 + 52 = 219; 219 + 41? No, wait the data is 82, 45, 43, 52, 41, 65, 38, 67, 88, 59, 54. So the numbers are: 38, 41, 43, 45, 52, 54, 59, 65, 67, 82, 88. Wait, 82, 45, 43, 52, 41, 65, 38, 67, 88, 59, 54. Let's list all: 38, 41, 43, 45, 52, 54, 59, 65, 67, 82, 88. Now sum: 38 + 41 = 79; +43=122; +45=167; +52=219; +54=273; +59=332; +65=397; +67=464; +82=546; +88=634. So sum is 634. Number of terms: 11. So mean is 634 / 11 ≈ 57.64. The given mean in the image (127.6) is incorrect.

Step3: Calculate the Median

For a data set with \(n = 11\) (odd number of values), the median is the \((\frac{n + 1}{2})\)-th term. \(\frac{11 + 1}{2} = 6\)-th term. The sorted data is \(38, 41, 43, 45, 52, 54, 59, 65, 67, 82, 88\). The 6th term is 54. So median is 54 (this part in the image is correct).

Step4: Calculate the Mode

The mode is the value that appears most frequently. In this data set, all values appear only once, so there is no mode (so "NONE" is correct here).

Step5: Calculate the Range

The range is the maximum value minus the minimum value. Maximum value is 88, minimum is 38. So range = \(88 - 38 = 50\). The given range in the image (52) is incorrect.

Answer:

• Mean: \(\approx 57.64\) (The given 127.6 is wrong)
• Median: \(54\) (Correct)
• Mode: \(NONE\) (Correct)
• Range: \(50\) (The given 52 is wrong)