Math Problem Statement

326 347 412 340 341 422 551 514 473 449 438 399 327 501 503 512 505 350 392 442A cellular phone company monitors monthly phone usage. The following data represent the monthly phone use in minutes of one particular customer for the past 20 months. Use the given data to answer parts​ (a) and​ (b). 326 347 412 340 341

422 551 514 473 449 438 399 327 501 503 512 505 350 392 442 Question content area bottom Part 1 ​(a) Determine the standard deviation and interquartile range of the data. s=

Solution

To calculate the standard deviation and the interquartile range (IQR) of the data, we need to follow these steps:

Part 1: Standard Deviation

The formula for the sample standard deviation ss is:

s=(xixˉ)2n1s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n - 1}}

Where:

  • xix_i represents each data point.
  • xˉ\bar{x} is the mean of the data.
  • nn is the total number of data points (in this case, n=20n = 20).

Part 2: Interquartile Range (IQR)

The interquartile range is the difference between the third quartile (Q3) and the first quartile (Q1):

IQR=Q3Q1IQR = Q3 - Q1

Let me calculate the standard deviation and IQR for the given data.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Statistics
Descriptive Statistics
Measures of Spread

Formulas

Standard Deviation: s = sqrt(Σ(xi - x̄)^2 / (n - 1))
Interquartile Range (IQR): IQR = Q3 - Q1

Theorems

Empirical Rule for Standard Deviation
IQR as a Measure of Dispersion

Suitable Grade Level

Grades 10-12