**Category 56 Example 1** - mental math

Compare the length of the line segment between two points. The longest length is from 2002 to 2003.

**Category 56 Example 2** - mental math

Read and add the length of the horizontal lines. 5 to 10 is 5. 20 to 30 is 10. 5 plus 10 is 15.

**Category 56 Example 3** - no calculation

Match the sequence of events in the question to the flow of events on the graphs in the answer choices.

**Category 57 Example 1 Question 1 **- no calculation

From the graph, read the grams of sugar for carbohydrate = 60.

**Category 57 Example 1 Question 2 **– mental math

From the graph, read the two values. Sugar for carbohydrate = 70 on the line is approximately 58. Sugar for carbohydrate = 70 on the graph is approximately 68. Approximate difference is 10.

**Category 58 Example 1** - mental math

Look at the heights of the two bars for each month. In January and May both the bars are relatively shorter than in Feb. and April. This eliminates answer choices A and D. It is apparent that the total number of employees for April is greater than in Feb. If unsure then the total number of employees for the two remaining months can be determined using mental math. For Feb.: 6 plus 15 is 21. For April: 10 plus 13 is 23.

**Category 59 Example 1** - mental math

Count the number of dots for 80, 100, and 120 minutes.

**Category 59 Example 2 Question 1 **– mental math

Count the frequency of the bars for 3 or more children. 10 (bar 3) plus 0 (bar 4) is 10 plus 5 (bar 5) is 15. The ratio of 15 to 60 should be apparent as 1:4.

**Category 62 Example 1** - mental math

Sort the numbers least to greatest and count the numbers in the data set. Since there are 10 numbers, the median can be determined using mental math as between 5th and 6th number. These numbers are 12 and 14. The average of 12 and 14 is 13.

**Category 62 Example 2** - no calculation

Sort the number of students from least to greatest. Since there are 5 numbers, the median is the 3rd number = 163 students. This corresponds to year 2012.

**Category 62 Example 3** **Question 1** - mental math

The median of 21 can be determined using mental math as 11th student. From top to bottom, count the number of students till the row containing the 11th student is reached. 1 (51-60) plus 4 (61-70) is 5 plus 3 (71-80) is 8 plus 8 (81-90) is 16. Hence, the median score range is between 81-90.

**Category 62 Example 3** **Question 2** - mental math

Continue from Question1 above. The median score can be any integer in the median score range = 81-90, hence, any integer from 81 to 90.

**Category 63 Example 1** - mental math

The median of 50 can be determined using mental math as between 25th and 26th person. From left to right, count the frequency of each bar till the bar containing the 25th to 26th person is reached. 5 (bar 1) plus 13 (bar 2) is 18 plus 12 (bar 3) is 30. Hence, the median number of movies is in bar 3.

**Category 63 Example 2** - mental math

The median of 40 can be determined using mental math as between 20th and 21st adult. From left to right, count the frequency of each bar till the bar containing the 25th to 26th adult is reached. 2 (bar 0 to less than 5) plus 10 (bar 5 to less than 10) is 12 plus 12 (bar 10 to less than 15) is 24. Hence, the median number of times is in bar 10 to less than 15. Median can be any integer from 10 to less than 15.

**Category 63 Example 3** - mental math

The median of 21 can be determined using mental math as the 11th kid. Count the dots from left to right till the 11th kid is reached. 5 (ride = 1) plus 4 (ride = 2) is 9 plus 3 (ride = 3) is 12. Hence, the median number of rides = 3.

**Category 64 Example 1** - no calculation

The median can be directly read from the box plot.

**Category 64 Example 2** - mental math

The median of 79 can be determined using mental math as 40th adult.

The numbers in the table can be added using mental math from left to right till the 40th adult is reached. 5 (rating 1) plus 22 (rating 20 is 27 plus 11 (rating 3) is 38. The next number is 11 and must contain the median. This is for rating = 4. This eliminates choices C and D.

Determine Q1. There are 39 numbers on each side of the median. Count from left to right till the middle number 20 is reached. 5 (rating 1) plus 22 (rating 2) is 27 and must contain the median. This rating is for rating = 2. Hence, contain Q1 = 2. This eliminates answer choice B.

**Category 65 Example 1 **- no calculation

Sort the numbers from least to greatest. The most often recurring number is mode.

**Category 66 Example 1 **

Spot the lowest and the highest number in each data set. It is apparent that the difference between the numbers is greater in Set A than in Set B. Hence, the range and the standard deviation of Set A is greater than Set B.

**Category 68 Example 1 **- no calculation

Based on the key points decide which sample is random and has the appropriate sample set.

**Category 68 Example 2 **- no calculation

Based on the key points decide which sample is random and has the appropriate sample set.

**Category 68 Example 3 **- mental math

Margin of error can be determined using mental math. 73 minus 4.5 is 68.5 and 73 plus 4.5 is 77.5.

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