Statistics

Question 1

What is the model/mode?

Answer 1

The data that appears the most frequently

Question 2

How do you calculate an estimate for the mean when given a table of ranges + frequency rather than exact numbers?

Answer 2

Use the midpoint of the ranges given and do rest as usual

Question 3

What does model class mean?

Answer 3

Which group/range of data is highest in frequency?

Question 4

What is positive correlation?

Answer 4

A slope/line of best fit that goes upwards

Question 5

What is negative correlation?

Answer 5

A slope/line of best fit that goes downwards

Question 6

How to draw a frequency polygon for a table of ranges + frequency?

Answer 6

1. Use the midpoints of the ranges and plot them on x axis
2. The frequency will be your y axis
3. The midpoint and frequency will be your coordinates (x being midpoint and frequency being the y coordinate)
4. Draw straight lines between the Xs

Question 7

How to draw a box plot?

Answer 7

1. The start and end of your box plot will be the lowest and highest values
2. The median of the data will be the middle of your box plot
3. The median of the midpoint and lowest value will make your lower quartile (not including the midpoint in the range)
4. The median of the midpoint and highest value will make your upper quartile (not including the midpoint in the range)
   5, Join up a box between lower midpoint and upper midpoint

Question 8

How to easily find your median if you have an odd amount of data?

Answer 8

Amount of data+1 / 2

Question 9

There are two things you want to compare when comparing a box plot, what are they?

Answer 9

The median, interquartile range which means the data is more spread out

Question 10

What is the distance between the lower and upper quartile called?

Answer 10

The interquartile range

Question 11

What is the difference between frequency and cumulative frequency?

Answer 11

Frequency is how many times a value occurred whilst cumulative frequency represents the total of all frequencies in a dataset

Question 12

How to draw a cumulative frequency graph?

Answer 12

1. Calculate cumulative frequencies (add the frequencies one by one as you go down the table)
2. The data on the right side of the range is your x axis whilst your cumulative frequencies are going to be seen on y axis
3. Plot points using coordinates, y coordinates being cumulative frequency and x coordinates being corresponding “right side of range” values
4. Draw a smooth curve starting from zero and joining all the points

Question 13

How to find answers for questions on cumulative frequency graphs like “find an estimate for the number of lorries with a speed of more than 90km/h” ?

Answer 13

1. Find the speed 90km/h on your x axis and go up until you hit the curved line
2. Find corresponding y value to that point in the line you hit
3. That is the estimated amount of lorries which was going 90km/h, so if it was 84 and there were 100 lorries in total in the data set, the amount of lorries going faster than 90km/h would be 100 - 84 which is 16 lorries

Question 14

How to find median on cumulative frequency graphs? E.g “find the speed of the median lorry”

Answer 14

1. Find median of final accumulated frequency on y axis, e.g if 100, median would be 50
2. Find the corresponding speed of that median on the curved line, it will be on x axis.

Question 15

How to find lower, upper and interquartile range on cumulative frequency graph?

Answer 15

Once you find the median of the final accumulated frequency, you are able to find all of these

Question 16

What is the formula needed when drawing a histogram?

Answer 16

Frequency Density = Frequency / Class Width

Question 17

How to find the parts of the Frequency Density formula that is used for histograms?

Answer 17

Frequency = Frequency on the table
Class width = How big the range is in the table

Question 18

What is a histogram and how to draw it?

Answer 18

A histogram is similar to a bar chart, the width of the rectangle on the x axis is the class width whilst the height on the y axis is the frequency density (f.d = freq / c.w)

Question 19

How to solve questions in histograms like “Work out an estimate for the number of cars with a speed of more than 85 km/h” ?

Answer 19

Find 85 km/h on the x axis and realize that the cube it is in can be split into equal parts, use this to find an estimate of the cars that are travelling more than 85 km/h

Question 20

How to work out a reverse mean question? (E.g. about mean scores scored between men, woman and children and we have to figure out the mean of what women scored with some missing data)

Answer 20

1. Find the amount of points scored by men and children
2. Find the total amount of points scored
3. Total amount of points scored - amount of points scored by men and children = amount of points scored by women
4. Work out the mean (amount of points scored by women / amount of women)