14.c Median, Mode, Range

Question 1

What is the “median”?

Answer 1

The value that is in the middle of the arranged set.

Question 2

What is the median of: [ -8, -1, 3, 5, 6, 9, 10 ] ?

Answer 2

The median is 5

Question 3

What is the median of: [ -8, -1, 3, 5, 6, 9, 10, 14 ] ?

Answer 3

The median is 5.5

As the set is even, you have to find the middle of the numbers, 5 and 6

Question 4

What is the difference in median between a set with an odd number of terms and a set with an even number of terms?

Answer 4

In a set with an odd number of terms, place the terms in numerical order and pick the middle number.

In a set with an even number of terms, place the terms in numerical order and find the mid-point of the two middle numbers.

Question 5

In very large odd number sets, how can you easily determine where the median is placed?

Answer 5

if it has “n” terms:

(n + 1) / 2

This is the PLACE of the median, NOT the median itself!

Question 6

In very large even number sets, how can you easily determine where the median is placed?

Answer 6

if it has “n” terms:

The AVERAGE of:
n / 2 and (n + 2) / 2

This is the PLACE of the median, NOT the median itself!

Question 7

Solve:

Answer 7

Question 8

In an evenly spaced set, the mean of the set is equal to the _______________

Answer 8

In an evenly spaced set, the mean of the set is equal to the MEDIAN OF THE SET

Question 9

Solve:

Answer 9

MEAN = MEDIAN

Question 10

Solve:

Answer 10

To solve this, order numerically and try to see if x placed at the start of end of the set would have any impact on the median, if not you know the median without even knowing the value of the variable!

In this case, the median is “10” regardless of the scenario!

Question 11

What is the “mode”?

Answer 11

The number that appears most frequently in a data set

Question 12

Can there be more than one mode in a data set?

Answer 12

Yes!

If two numbers appear the same amount of times, they are both the mode.

eg. [ 1, 2, 2, 2, 3, 3, 3, 5 ] - both 2 and 3 are the modes

Question 13

Can there be no mode in a data set?

Answer 13

Yes!

If every number occurs the same number of times as the others, thee is no mode!

eg. [ 1, 2, 3, 4, 5, 6, 7 ]

Question 14

What is the range of a data set?

Answer 14

Highest Number in set - Lowest Number in set

Question 15

Solve:

Answer 15

Range = 65 - 30 = 35 minutes

If the range doubles, it has to become 70 minutes.

So Lowest value + 70 = highest value,

30 + 70 = 100

Question 16

If set A has a range of P, and set B has a range of Q,

if P is smaller than or equal to Q,

Then the least possible range of the two sets combined will be _____

Answer 16

If set A has a range of P, and set B has a range of Q,

if P is smaller than or equal to Q,

Then the least possible range of the two sets combined will be Q

Question 17

Solve:

Answer 17

Question 18

How would you find the maximum possible range when two or more sets are combined?

Answer 18

greatest possible range = G - S

Where G is the greatest possible value in the set, and S is the least possible value in the set

Question 19

Explain how you would solve this:

Answer 19

Greatest - Smallest

Greatest:
999 < T < 10,000 = 8999 (range)

Smallest:
2000 (Gammia province)

Greatest - Smallest = 8999 - 2000 = 6999

Question 20

How would you calculate the range of the sum of reciprocals of integers (fractions)?

Answer 20

1. Determine how many fractions are in the set
2. Identify the smallest fraction in the set and the largest fraction in the set
3. Multiply both (smallest and largest) fractions by the number of fractions in the set

Question 21

Explain how you would solve this:

Answer 21

Find number of integers in the set.

Identify smallest and largest, multiply by the #.