Data: graphs, mean & range for Grade 4

1 · Scaled bar graphs

When the numbers are big, the side counts by 10s (or 5s, or 100s). A bar that stops between two lines is read by halving: between 40 and 50 is 45.

Monday: 64 (just past 60). Tuesday: 26. Wednesday: 21. Thursday: 45.

2 · Best day minus worst day

"How many more were sold on the best day than the worst?" Best is Monday (64), worst is Wednesday (21). 64 − 21 = 43.

Find the tallest and shortest first, then subtract.

3 · Totals and halves

Add every bar for the total: 64 + 26 + 21 + 45 = 156. "Which days together sold more than half?" Half of 156 is 78; Monday + Thursday = 109, so yes.

4 · Pictographs with big keys

Here ★ = 10 stickers, so a half star is 5. Ava has 4 stars and a half: 45. Kim has 5 and a half: 55.

Read the key, then count by the key. Half symbols are half the key.

5 · Line plots with fractions

A line plot counts how often each measurement happened. The marks can be halves or quarters. Four plants are 4 inches tall (4 Xs); how many are taller than 4? 2 + 2 = 4.

How many plants in all? Count every X: 1 + 3 + 4 + 2 + 2 = 12.

6 · Tables

A table is a graph without bars. Read across the row you need. Sam scored 53. Who scored the least? Ava, 38.

Tables often ask for a difference: Sam − Ava = 53 − 38 = 15.

7 · Range: largest minus smallest

The range tells how spread out the numbers are: largest − smallest. For 45, 26, 44, 41, 50: largest 50, smallest 26, range 24.

Find the two ends first. The middle numbers do not matter for the range.

8 · Mean: share it out evenly

The mean (average) is what each would get if the total were shared evenly. Scores 42, 39, 38, 53: total 172. Four scores, so 172 ÷ 4 = 43.

The dashed line shows the mean: the bars above it would fill the gaps below it.

9 · Mean of a graph

You can average bars too. Cupcakes: 64 + 26 + 21 + 45 = 156, over 4 days: 156 ÷ 4 = 39 a day.

The mean is always between the smallest and largest value. If it is not, recheck your adding.

10 · A missing value from the mean

"The mean of 3 numbers is 20. Two of them are 15 and 22. What is the third?" Total must be 3 × 20 = 60. 60 − 15 − 22 = 23.

Mean × count = total. Then subtract what you know.

11 · Data in words

Tests often skip the picture: "A graph shows sales: Mon 59, Tue 54, Wed 21. How many more on the best day than the worst?" 59 − 21 = 38.

Write the numbers in a quick list, mark the biggest and smallest, then answer.

12 · Which statement is true?

Some questions give four sentences about a graph. Check each against the numbers. "Tuesday sold more than Wednesday" (26 vs 21: true). "Thursday sold twice Tuesday" (45 vs 52: false).

Check every choice, even after one sounds right.