Averages, Ranges & Data Flashcards

All 42 cards in this deck

What is the mode of a set of data?

The value that occurs most often.

What is the median of a set of data?

The middle value when the data are put in order of size.

What are the steps to find the median of a list of values?

e.g. $7, 3, 5, 9, 4$

1. Put the values in order of size: $3, 4, 5, 7, 9$
2. Find the middle value: $5$

How do you find the median when there is an even number of values?

e.g. $5, 7$ are the two middle values

Add the two middle values and divide by 2.
$(5+7)\div 2 = 6$

True or false? You can find the median by taking the middle number of the list as it is written.

False. You must put the numbers in order of size first.

True or false? A set of data can have more than one mode.

True. If two or more values are equally most common, each is a mode.

What are the steps to find a missing value when you know the mean?

e.g. four numbers have mean $10$; three of them add to $32$

1. Total $=$ mean $\times$ number of values: $10\times4=40$
2. Subtract the values you know: $40-32=8$
3. The missing value is $8$

True or false? The mean of two groups is found by adding the two group means and dividing by 2.

False. That only works if both groups are the same size; otherwise use total of all values ÷ total number of values.

If one value in a data set is replaced by a larger value, what happens to the mean?

The mean increases, because the total increases while the number of values stays the same.

True or false? If you add a new value equal to the current mean, the mean stays the same.

True. The total and the number of values both grow in proportion.

In a frequency table of discrete data, how do you find the mode?

Write down the data value (not the frequency) with the highest frequency.

True or false? In a frequency table, if the highest frequency is 15 then the mode is 15.

False. The mode is the data value that has that frequency, not the frequency itself.

What formula gives the mean from a frequency table?

Mean $=\dfrac{\Sigma fx}{\Sigma f}$

What are the steps to find the mean from a frequency table?

e.g. value $1$ (frequency $2$), value $4$ (frequency $3$)

1. Multiply each value by its frequency: $1\times2=2$, $4\times3=12$
2. Add them: $\Sigma fx = 14$; add frequencies: $\Sigma f = 5$
3. Divide: $14\div5=2.8$

How do you find the position of the median from a frequency table?

e.g. total frequency $\Sigma f = 19$

Work out $\dfrac{\Sigma f + 1}{2}$ to get the position, then count up the frequencies to that position.
$(19+1)\div2 = 10$th value

True or false? To find the mean from a frequency table you divide $\Sigma fx$ by the number of rows in the table.

False. You divide by $\Sigma f$, the total frequency.

What is the modal class of a grouped frequency table?

The class interval with the highest frequency.

How do you find the midpoint of a class interval?

e.g. $10 \le t < 20$

Add the two end values and divide by 2.
$(10+20)\div2 = 15$

What are the steps to estimate the mean from a grouped frequency table?

e.g. $0<t\le10$ (frequency $3$), $10<t\le20$ (frequency $2$)

1. Find each midpoint: $5$ and $15$
2. Work out $\Sigma fx$: $5\times3+15\times2=45$
3. Divide by $\Sigma f$: $45\div5=9$

Why is the mean from a grouped frequency table only an estimate?

Because the exact data values are unknown, so midpoints are used to represent each class.

True or false? The modal class of a grouped frequency table is the class with the largest values.

False. It is the class with the highest frequency.

True or false? You can work out the exact range from a grouped frequency table.

False. You can only estimate it, since the largest and smallest actual values are not known.

What is the range of a set of data?

Largest value $-$ smallest value.

What does the range measure?

The spread of the data, not an average.

True or false? The range is written as two numbers, e.g. "12 to 22".

False. The range is a single number found by subtracting: $22-12=10$.

What is an outlier?

A value that is much larger or much smaller than the rest of the data.

What effect does an outlier have on the range?

It makes the range much larger, so the range no longer represents the typical spread.

True or false? A smaller range means the data are more consistent.

True. Less spread means the values are closer together.

When comparing two data sets, what two things should your comparison include?

A comparison of an average (e.g. the medians) and a comparison of the spread (the ranges), both in context.

True or false? Writing "the median for boys is 8 and the median for girls is 6" is enough to compare the data sets.

False. You must compare them, e.g. "the boys' median is greater than the girls' median".

Which average is most affected by an extreme value (outlier)?

The mean, because every value is used in the total.

When is the median a better average than the mean?

When the data contain extreme values or outliers, since the median is not affected by them.

Which average must you use for non-numerical (categorical) data such as colours?

The mode.

True or false? A larger range for one group means that group's values are generally higher.

False. A larger range means more spread out (less consistent), not higher.

What is a population in statistics?

The whole group that is being studied.

What is a sample?

A smaller part of the population that is selected and studied.

Give one advantage of taking a sample rather than surveying the whole population.

It is quicker and cheaper.

What makes a sample unreliable for drawing conclusions about a population?

Being too small or not representative (biased).

How do you estimate a population total from a sample proportion?

e.g. $3$ of $20$ sampled are left-handed, population $400$

Multiply the sample proportion by the population size.
$\frac{3}{20}\times400 = 60$

True or false? A sample of 10 students from one class can reliably represent all students in a school.

False. The sample is too small and taken from only one class, so it is not representative.

What are the steps to work out the mean of a list of values?

e.g. $4, 6, 8, 6$

1. Add all the values: $4+6+8+6=24$
2. Count how many values there are: $4$
3. Divide the total by the count: $24\div4=6$

True or false? The mean of a list of values must be one of the values in the list.

False. The mean can be a value not in the list, e.g. the mean of $3$ and $4$ is $3.5$.