A sample of 33 accounting students recorded the number of...

Name: Problem 10, Chapter 2: Statistics for Business and Economics: Global Edition
Uploaded: 2022-01-14T16:53:45-08:00
Duration: 4 min 27 s
Channel: Jon Southam
Description: A sample of 33 accounting students recorded the number of hours spent studying the course material during the week before the final exam. The data are stored in the data file Study. a. Compute the sample mean. b. Compute the sample median. c. Comment on symmetry or skewness. d. Find the five-number summary for this data.

A sample of 33 accounting students recorded the number of hours spent studying the course material during the week before the final exam. The data are stored in the data file Study. a. Compute the sample mean. b. Compute the sample median. c. Comment on symmetry or skewness. d. Find the five-number summary for this data.

A sample of 33 accounting students recorded the number of hours spent studying the course material during the week before the final exam. The data are stored in the data file Study.
a. Compute the sample mean.
b. Compute the sample median.
c. Comment on symmetry or skewness.
d. Find the five-number summary for this data.

Key Concepts

Sample Mean

The sample mean is a measure of central tendency that represents the average of all observed values in a sample. It is calculated by summing up all the individual data points and then dividing this total by the number of observations. This metric provides a simple summary of the overall level of the data set.

Sample Median

The sample median is the middle value in an ordered data set. When the data are arranged from smallest to largest, the median divides the data into two equal halves. Unlike the mean, the median is not affected by extremely high or low values, making it a robust measure of central tendency in the presence of outliers.

Skewness and Symmetry

Skewness refers to the degree of asymmetry found in a distribution of data. A symmetrical distribution has an equal spread around the central value, while a skewed distribution has a longer tail on one side. The degree and direction of skewness can provide insights into the nature of the data distribution and potential outliers.

Five-Number Summary

The five-number summary is a set of descriptive statistics that provides a quick overview of a data set. It comprises the minimum, first quartile (Q1), median (second quartile, Q2), third quartile (Q3), and maximum values. These five statistics offer insights into the range, central location, and variability within the sample.

Transcript

00:02 We're looking at salaries of five accounting graduates who took positions in public accounting last year.

00:12 And we're looking at the skewness of these salaries.

00:17 So we're asked to find the mean, median, and standard deviation.

00:22 I have that right here.

00:24 And i used the spreadsheet to do it for me, but that's because those are pretty, pretty, standard things to do anyway and the standard deviation just as a reminder that's the sample standard deviation that the population so there's those values the skewness using pearson's method so here's pearson's methods i'll do that way here be we're gonna do is use this formula so we have equals we have three times we're gonna follow the formula it's the mean minus the median so equals that cell minus this cell all divided by the standardiation.

01:20 So that's why we had to get all those three values.

01:26 What happened here? oh, you have to put a parenthesis a star multiplication between the three in the parentheses.

01:41 Okay, so it's pretty close to one.

01:43 So these are values between negative 3 and 3.

01:47 So this is relatively close to 0.

01:48 So not a ton of skewness there based on pearson's.

01:51 Let's check out the software.

01:54 So for that one, we need to do a little bit of work beforehand, namely this bit here, the sum of the difference.

02:02 So we take each data point, take the mean from it, divide by a steering deviation.

02:08 And we cube all those, and then we take those sums.

02:10 So the spreadsheet is nice to display that.

02:14 So here's the mean, which is equal to that value.