# 2.5 Measures of the center of the data  (Page 4/11)

 Page 4 / 11

## Try it

Maris conducted a study on the effect that playing video games has on memory recall. As part of her study, she compiled the following data:

Hours Teenagers Spend on Video Games Number of Teenagers
0–3.5 3
3.5–7.5 7
7.5–11.5 12
11.5–15.5 7
15.5–19.5 9

What is the best estimate for the mean number of hours spent playing video games?

Find the midpoint of each interval, multiply by the corresponding number of teenagers, add the results and then divide by the total number of teenagers
The midpoints are 1.75, 5.5, 9.5, 13.5,17.5.
Mean = (1.75)(3) + (5.5)(7) + (9.5)(12) + (13.5)(7) + (17.5)(9) = 409.75

Data from The World Bank, available online at http://www.worldbank.org (accessed April 3, 2013).

“Demographics: Obesity – adult prevalence rate.” Indexmundi. Available online at http://www.indexmundi.com/g/r.aspx?t=50&v=2228&l=en (accessed April 3, 2013).

## Chapter review

The mean and the median can be calculated to help you find the "center" of a data set. The mean is the best estimate for the actual data set, but the median is the best measurement when a data set contains several outliers or extreme values. The mode will tell you the most frequently occuring datum (or data) in your data set. The mean, median, and mode are extremely helpful when you need to analyze your data, but if your data set consists of ranges which lack specific values, the mean may seem impossible to calculate. However, the mean can be approximated if you add the lower boundary with the upper boundary and divide by two to find the midpoint of each interval. Multiply each midpoint by the number of values found in the corresponding range. Divide the sum of these values by the total number of data values in the set.

## Formula review

$\mu =\frac{\sum fm}{\sum f}$ Where f = interval frequencies and m = interval midpoints.

Find the mean for the following frequency tables.

1. Grade Frequency
49.5–59.5 2
59.5–69.5 3
69.5–79.5 8
79.5–89.5 12
89.5–99.5 5
2. Daily Low Temperature Frequency
49.5–59.5 53
59.5–69.5 32
69.5–79.5 15
79.5–89.5 1
89.5–99.5 0
3. Points per Game Frequency
49.5–59.5 14
59.5–69.5 32
69.5–79.5 15
79.5–89.5 23
89.5–99.5 2

Use the following information to answer the next three exercises: The following data show the lengths of boats moored in a marina. The data are ordered from smallest to largest:

• 16
• 17
• 19
• 20
• 20
• 21
• 23
• 24
• 25
• 25
• 25
• 26
• 26
• 27
• 27
• 27
• 28
• 29
• 30
• 32
• 33
• 33
• 34
• 35
• 37
• 39
• 40

Calculate the mean.

Mean: 16 + 17 + 19 + 20 + 20 + 21 + 23 + 24 + 25 + 25 + 25 + 26 + 26 + 27 + 27 + 27 + 28 + 29 + 30 + 32 + 33 + 33 + 34 + 35 + 37 + 39 + 40 = 738;

$\frac{738}{27}$ = 27.33

Identify the median.

Identify the mode.

The most frequent lengths are 25 and 27, which occur three times. Mode = 25, 27

Use the following information to answer the next three exercises: Sixty-five randomly selected car salespersons were asked the number of cars they generally sell in one week. Fourteen people answered that they generally sell three cars; nineteen generally sell four cars; twelve generally sell five cars; nine generally sell six cars; eleven generally sell seven cars. Calculate the following:

sample mean = $\overline{x}$ = _______

median = _______

4

mode = _______

## Bringing it together

Javier and Ercilia are supervisors at a shopping mall. Each was given the task of estimating the mean distance that shoppers live from the mall. They each randomly surveyed 100 shoppers. The samples yielded the following information.

Javier Ercilia
$\overline{x}$ 6.0 miles 6.0 miles
$s$ 4.0 miles 7.0 miles
1. How can you determine which survey was correct ?
2. Explain what the difference in the results of the surveys implies about the data.
3. If the two histograms depict the distribution of values for each supervisor, which one depicts Ercilia's sample? How do you know?
4. If the two box plots depict the distribution of values for each supervisor, which one depicts Ercilia’s sample? How do you know?

Use the following information to answer the next three exercises : We are interested in the number of years students in a particular elementary statistics class have lived in California. The information in the following table is from the entire section.

Number of years Frequency Number of years Frequency
Total = 20
7 1 22 1
14 3 23 1
15 1 26 1
18 1 40 2
19 4 42 2
20 3

What is the IQR ?

1. 8
2. 11
3. 15
4. 35

a

What is the mode?

1. 19
2. 19.5
3. 14 and 20
4. 22.65

Is this a sample or the entire population?

1. sample
2. entire population
3. neither

b

#### Questions & Answers

mean 0 and standard deviation 1 .using area table find P(X>3)
Naeem Reply
what is terms data?
Mohsin Reply
define the types of data?
Mohsin
define the number of classes?
Mohsin
define the class limt?
Mohsin
define the class frequency and class interval ?
Mohsin
define class boundaries
George
Your home address nominal Interval ratio ordinal
MD
home address is nominal
Awel
what is axioms of probability
Khaleed Reply
characteristics of statistic
Safi Reply
a measure of cntral tendency is a quantitative value that tends to locate in some sense the middle of a set of data
khan Reply
in a large metropolitan area
Vernon Reply
a lecturer claims that his students score an average of 55 marks in their statistics test. the object supervisor wants to know wether the lecturer's claims is acceptable or not.what is the posible tail of the test?
Karen
2
J-zil
the best sampling method for A school has a total of 100 teachers. Each teacher in the school is given a number and then a random sample of 35 teachers is obtained.
Nurhaznissah Reply
what the best sampling method for A school has a total of 100 teachers. Each teacher in the school is given a number and then a random sample of 35 teachers is obtained.
Nurhaznissah
option please
Dewan
systematic
Dewan
any one send me the notes of these chpt if possible introduction to statistics measure of centeral tendency or average measure of dispensation moments and skewness presentation of data
Aqsa Reply
Kindly send me these notes.
Naheed
what is a regression, and what is it primarily used for
Denisha Reply
assume the sample populations do not have equal standard deviations and use the 0.05 significance level
Nokuthula Reply
what is the solution to this question?
Manbyen Reply
hi
Dewan
hello
Learn
hi please tell
Dewan
The controls that are usually used are
Rushikesh Reply
what is math
Rushikesh
the controls that are usually used in quality controls and also controls a process is key tool used in run chat, control chat and design of experiment etc.,
Sravanthi
mean is number that occurs frequently in a giving data
Chinedu Reply
That places the mode and the mean as the same thing. I'd define the mean as the ratio of the total sum of variables to the variable count, and it assigns the variables a similar value across the board.
Samsicker
what is mean
John Reply
what is normal distribution
RAHAT Reply

### Read also:

#### Get Jobilize Job Search Mobile App in your pocket Now!

Source:  OpenStax, Introductory statistics. OpenStax CNX. May 06, 2016 Download for free at http://legacy.cnx.org/content/col11562/1.18
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Introductory statistics' conversation and receive update notifications? By By By OpenStax By Steve Gibbs By OpenStax By David Martin By Sandhills MLT By By Jemekia Weeden By OpenStax By OpenStax By OpenStax