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Holt Algebra 1
10-3 Data Distributions
Warm UpSimplify each expression.
1. 2. 102 – 53
3. Use the data below to make a stem-and-leaf
plot. 7, 8, 10, 18, 24, 15,
17, 9, 12, 20, 25, 18, 21, 12
60 49
Holt Algebra 1
10-3 Data Distributions
10-3 Data Distributions
Holt Algebra 1
Holt Algebra 1
10-3 Data Distributions
• The mean is the sum of the values in the set divided by the number of values in the set.
• The median the middle value when the values are in numerical order, or the mean of the two middle values if there are an even number of values.
• The mode is the value or values that occur most often. There may be one mode or more than one mode..
The range of a set of data is the difference between the least and greatest values in the set.
Holt Algebra 1
10-3 Data Distributions
Example 1A: Finding Mean, Median, Mode, and Range of a Data Set
Find the mean, median, mode, and range of the data set.
The number of hours students spent on a research project: 2, 4, 10, 7, 5
median: 2, 4, 5, 7, 10The median is 5.
range: 10 – 2 = 8
mode: none
Write the data in numerical order.
Add all the values and divide by the number of values.
There are an odd number of values. Find the middle value.
No value occurs more than once.
mean:
Holt Algebra 1
10-3 Data Distributions
Check It Out! Example 1c Find the mean, median, mode, and range of the data set.
12, 18, 14, 17, 12, 18
median: 12, 12, 14, 17, 18, 18 The median is 15 .
mean:
mode: 12, 18
range: 18 – 12 = 6
Holt Algebra 1
10-3 Data Distributions
A value that is very different from other values in the set is called an outlier..
Holt Algebra 1
10-3 Data Distributions
Example 2: Choosing a Measure of Central Tendency
Rico scored 74, 73, 80, 75, 67, and 55 on six history tests. Use the mean, median, and mode of his scores to answer each question.
mean ≈ 70.7 median = 73.5 mode = none
A. Which value gives Rico’s test average?
The average of Rico’s scores is the mean, 70.7.
B. Which values best describes Rico’s scores?Median; most of his scores are closer to 73.5 than to 70.6.
The mean is lower than most of Rico’s scores because he scored a 55 on one test. Since there is no mode, it is not a good description of the data.
Holt Algebra 1
10-3 Data Distributions
Quartiles divide a data set into four equal parts. Each quartile contains one-fourth of the values in the set. The interquartile range (IQR) is the difference between the upper and lower quartiles. The IQR represents the middle half of the data.
Holt Algebra 1
10-3 Data Distributions
Holt Algebra 1
10-3 Data Distributions
A box-and-whisker plot can be used to show how the values in a data set are distributed.
The minimum is the least value that is not an outlier. The maximum is the greatest value that is not an outlier.
You need five values to make a box-and-whisker plot: the minimum, first quartile, median, third quartile, and maximum.
Holt Algebra 1
10-3 Data Distributions
Mathematically, any value that is 1.5(IQR) less than the first quartile or 1.5(IQR) greater than the third quartile is an outier.
Helpful Hint
Holt Algebra 1
10-3 Data Distributions
Example 3: Sports Application
The number of runs scored by a softball team at 19 games is given. Use the data to make a box-and-whisker plot.
3, 8, 10, 12, 4, 9, 13, 20, 12, 15, 10, 5, 11, 5, 10, 6, 7, 6, 11
Step 1 Order the data from least to greatest.
3, 4, 5, 5, 6, 6, 7, 8, 9, 10, 10, 10, 11, 11, 12, 12, 13, 15, 20
Step 2 Identify the five needed values and determine whether there are any outliers.
Holt Algebra 1
10-3 Data Distributions
Example 3 Continued
3, 4, 5, 5, 6, 6, 7, 8, 9, 10, 10, 10, 11, 11, 12, 12, 13, 15, 20
Q1
6
Q3
12
Q2
10
Minimum
3
Maximum
20
IQR: 12 – 6 = 6 1.5(6) = 9
6 – 9 = –3 12 + 9 = 21
No values are less than –3 or greater than 21, so there are no outliers.
Holt Algebra 1
10-3 Data Distributions
Example 3 Continued
Half of the scores are between 6 and 12 runs per game. One-fourth of the scores are between 3 and 6. The greatest score earned by this team is 20.
0 8 16 24
Median
First quartile Third quartile
● ●●● ●
Minimum Maximum
Holt Algebra 1
10-3 Data Distributions
Check It Out! Example 3
Use the data to make a box-and-whisker plot.
13, 14, 18, 13, 12, 17, 15, 12, 13, 19, 11, 14, 14, 18, 22, 23
Step 1 Order the data from least to greatest.
11, 12, 12, 13, 13, 13, 14, 14, 14, 15, 17, 18, 18, 19, 22, 23
Step 2 Identify the five needed values and determine whether there are any outliers.
Holt Algebra 1
10-3 Data Distributions
11, 12, 12, 13, 13, 13, 14, 14, 14, 15, 17, 18, 18, 19, 22, 23
Q1
13
Q3
18
Q2
14
Minimum
11
Maximum
23
Check It Out! Example 3 Continued
IQR: 18 – 13 = 5 1.5(5) = 7.5
13 – 7.5 = 5.5 18 + 7.5 = 25.5
No values are less than 5.5 or greater than 25.5, so there are no outliers.
Holt Algebra 1
10-3 Data Distributions
Half of the data are between 13 and 18. One-fourth of the data are between 11 and 13. The greatest value is 23.
Check It Out! Example 3 Continued
8 16 24
Median
First quartile Third quartile
• ●•• •
Minimum Maximum
Holt Algebra 1
10-3 Data Distributions
Holt Algebra 1
10-3 Data Distributions
1. Find the mean, median, mode, and range of the data set.
Lesson Quiz: Part I
The number of hours Gerald mowed lawns in one week: 7, 3, 5, 4, 5
mean: 4.8; median: 5; mode: 5; range: 4
Holt Algebra 1
10-3 Data Distributions
Lesson Quiz: Part II
The following list gives times of Tara’s one-way ride to school (in minutes) for one week: 12, 23, 13, 14, 13. Use the mean, median, and mode of her times to answer each question.
mean = 15 median = 13 mode = 13
2. Which value describes the time that occurred most often? mode, 13
3. Which value best describes Tara’s ride time? Explain.Median or mode: 13; 13 occurred twice, and most times are near this value.
Holt Algebra 1
10-3 Data Distributions
Lesson Quiz: Part III
4. The number of inches of snow that fell during the last 8 winters in one city are given. Use the data to make a box-and-whisker plot.
25, 17, 14, 27, 20, 11, 29, 32
1115.5 22.5 28
32
Holt Algebra 1
10-3 Data Distributions
1. Find the mean, median, mode, and range of the data set.
Warm-Up
The number of hours Gerald mowed lawns in one week: 7, 3, 5, 4, 5
mean: 4.8; median: 5; mode: 5; range: 4