What is statistics used for?

Understanding chemical reactions

Which of the following statements is true about the mean, median, and mode?

They are measures of central tendency

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Introduction Quiz - CBSE Class 7 Mathematics

Free practice quiz: Introduction (CBSE Class 7 Mathematics). 16 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 7 Mathematics practice quiz has 16 multiple-choice questions on Introduction, and 16 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

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Statistics, Data and Range

Statistics means collecting, organising, presenting and interpreting data to draw useful conclusions.
A representative value, like mean, median or mode, describes the centre of the data.
Range shows how spread out the data is: highest value minus lowest value.

Range

\[\text{Range} = \text{Highest observation} - \text{Lowest observation}\]

All values equal

\[\text{Range} = a - a = 0\]

Common mistake: Subtracting the first and last numbers as written, without first finding the actual highest and lowest values.

Arithmetic Mean (Average)

Mean is the sum of all observations divided by the number of observations.
Every value affects the mean, so an outlier pulls the mean towards itself.
A few very high values make the mean larger than most of the data.

Mean

\[\bar{x} = \frac{\text{Sum of all observations}}{\text{Number of observations}}\]

Short form

\[\bar{x} = \frac{\sum x}{n}\]

Common mistake: Dividing by the largest value or forgetting to count every observation when finding n.

Median: The Middle Value

Arrange data in ascending order first. The median is the middle value.
It splits the data into equal halves: half the values lie below it, half above.
If n is even, the median is the average of the middle pair of values.

Common mistake: Picking the middle number without first arranging the data in ascending or descending order.

Mode: Most Frequent Value

Mode is the observation that occurs most often in the data.
Data with exactly a pair of modes is called bimodal; data can have several modes.
The mode changes when the frequencies of values change, such as adding repeats of another value.

Common mistake: Thinking every data set has exactly one mode. Ties give several modes, and if no value repeats, there is no mode.

Comparing Mean, Median, Mode

In a symmetric distribution, the mean, median and mode are all equal.
In skewed data, the mean is pulled towards the long tail, but the median stays near the centre.
So the median is preferred for skewed data with outliers, since it resists extreme values.

Symmetric data

\[\text{Mean} = \text{Median} = \text{Mode}\]

Common mistake: Believing the mean, median and mode are always equal. That is true only for symmetric data.

Exam tips

Always sort the data before finding the median or the mode.
Ask: is there an outlier? If yes, the mean is most affected.
Count the frequency of each value carefully to find every mode.

Beta: made with AI and checked by a second AI. A teacher has not reviewed it yet.

Sample questions

What is statistics used for?
Show answer
Answer: A. Collecting and analyzing data
Statistics is a branch of mathematics dealing with data collection, organization, analysis, interpretation, and presentation.
Which measure of central tendency divides a data set into two equal halves?
Show answer
Answer: B. Median
The median is the middle number of a data set, dividing the data into two equal parts.
Which of the following statements is true about the mean, median, and mode?
Show answer
Answer: D. They are measures of central tendency
Mean, median, and mode are all measures of central tendency used to summarize a set of data.
If a data set's numbers are mostly low with a few high outliers, which measure of central tendency is likely most affected?
Show answer
Answer: A. Mean
The mean is affected by outliers because it takes every value into account. High outliers can significantly increase the mean.
If a data set consists entirely of the same number, what is the range?
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Answer: A. 0
When all numbers in a data set are the same, the difference between the highest and lowest value (the range) is 0.