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7.5 Data Analysis
7.5.1 Descriptive Statistics
7.5.1.1 Measures of Central Tendency
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Measures of central tendency are statistical values that represent the center or
average
of a dataset.
What are the three main measures of central tendency?
Mean, median, and mode
Steps to calculate the mean of a dataset.
1️⃣ Sum all values in the dataset
2️⃣ Count the number of values
3️⃣ Divide the sum by the number of values
The mean is always the most accurate measure of central tendency.
False
Match the measure of central tendency with its definition:
Mean ↔️ The arithmetic average of all values
Median ↔️ The middle value when data is ordered
Mode ↔️ The most frequently occurring value
The mean is sensitive to
outliers
, which can distort its value.
The median uses all data points in its calculation.
False
The mode is particularly useful for summarizing
categorical
data.
Why are measures of central tendency used in data analysis?
To summarize and simplify data
The mean is affected by
skewed distributions
.
The median is not affected by
outliers
, making it robust for skewed data.
What is a disadvantage of using the mode as a measure of central tendency?
It may not be unique
How is the median calculated for a dataset with an even number of values?
Average the two middle values
Steps to calculate the mean of the dataset {2, 4, 6, 8, 10}.
1️⃣ Add all the values: 2 + 4 + 6 + 8 + 10 = 30
2️⃣ Count the number of values: 5
3️⃣ Divide the sum by the number of values: 30 / 5 = 6
What is the mean of the dataset {2, 4, 6, 8, 10}?
6
The mean uses all data points but is sensitive to
outliers
.
Measures of central tendency are statistical values that represent the
center
Match the measure of central tendency with its definition:
Mean ↔️ The arithmetic average of all values
Median ↔️ The middle value when data is ordered
Mode ↔️ The most frequently occurring value
The mean is sensitive to
outliers
.
The median is not affected by
outliers
The mode is always unique in a dataset.
False
What is the mean of the dataset {2, 4, 6, 8, 10}?
6
The median of the dataset {2, 4, 6, 8, 10} is
6
Measures of central tendency are used to summarize and compare
datasets
.
What is the mean of the dataset {2, 4, 6, 8}?
5
The median of the dataset {2, 4, 6, 8} is
5
The
mode
of the dataset {2, 4, 4, 6, 8} is 4.
Steps to calculate the mean
1️⃣ Add all values in the dataset
2️⃣ Count the number of values
3️⃣ Divide the sum by the number of values
What is the first step in calculating the mean of a dataset?
Add all values
To calculate the mean, you divide the sum of values by the number of
values
The sum of the dataset {2, 4, 6, 8, 10} is
30
.
How many values are in the dataset {2, 4, 6, 8, 10}?
5
What is the mean of the dataset {2, 4, 6, 8, 10}?
6
The mean of the dataset {2, 4,
6
, 8, 10} is 6.
The sum of the dataset {2, 4, 6, 8, 10} is
30
What is the sum of the values in the dataset {2, 4, 6, 8, 10}?
30
The dataset {2, 4, 6, 8, 10} contains
5
values.
What is the mean of the dataset {2, 4, 6, 8, 10}?
6
Steps to calculate the mean of a dataset
1️⃣ Add all the values in the dataset to get the sum of values
2️⃣ Count the number of values in the dataset
3️⃣ Divide the sum of values by the number of values
The mean is the
arithmetic
average of a dataset.
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