Math / Data & Statistics

QuestionEach dot in the following dot plot represents the number of chocolate chips in a single cookie in that box. a. Find the median of the data set:
Answer: Blank 1 b. Find the range of the data set:
Answer: Blank 2 c. Find the interquartile range:
Answer: Blank 3

Studdy Solution

STEP 1

What is this asking? We need to find the median, range, and interquartile range of the number of chocolate chips in cookies based on a dot plot. Watch out! Don't forget that each dot represents a cookie, so count them carefully!
Also, remember the difference between the range and the interquartile range.

STEP 2

1. Arrange the Data
2. Find the Median
3. Find the Range
4. Find the Quartiles
5. Calculate the Interquartile Range

STEP 3

Let's write out all the chip counts, remembering each dot is a cookie!
We have: $1, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 7, 9$ .
There are 13 data points in total.

STEP 4

Since we have an odd number of data points ( $13$ ), the median is simply the middle value.
We can find the middle value by counting $(13 + 1) / 2 = 7$ .
The 7th value in our ordered list is 4, so the median is $4$ .

STEP 5

The range is the difference between the largest and smallest values.
Our largest value is $9$ and our smallest is $1$ .
So, the range is $9 - 1 = 8$ .

STEP 6

To find the interquartile range, we first need the first quartile (Q1) and the third quartile (Q3).
Q1 is the median of the lower half of the data, and Q3 is the median of the upper half.

STEP 7

Since our dataset has $13$ values, the median, which is $4$ , is the 7th value.
The lower half of the data consists of the first six values: $1, 2, 3, 3, 4, 4$ .
Since there are an even number of values, the median is the average of the middle two: $(3 + 3) / 2 = 3$ .
So, Q1 is $3$ .

STEP 8

The upper half of the data consists of the values after the median: $4, 4, 5, 5, 6, 7, 9$ .
Again, there are an odd number of values, so the median is the middle value, which is $5$ .
So, Q3 is $5$ .

STEP 9

The interquartile range (IQR) is the difference between Q3 and Q1: $\text{IQR} = Q3 - Q1 = 5 - 3 = 2$ .

STEP 10

a. Median: $4$ b. Range: $8$ c. Interquartile Range: $2$

Was this helpful?

QuestionEach dot in the following dot plot represents the number of chocolate chips in a single cookie in that box. a. Find the median of the data set:
Answer: Blank 1 b. Find the range of the data set:
Answer: Blank 2 c. Find the interquartile range:
Answer: Blank 3

Studdy Solution

STEP 1

STEP 2

1. Arrange the Data
2. Find the Median
3. Find the Range
4. Find the Quartiles
5. Calculate the Interquartile Range

STEP 3

Let's write out all the chip counts, remembering each dot is a cookie!
We have: $1, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 7, 9$ .
There are 13 data points in total.

STEP 4

Since we have an odd number of data points ( $13$ ), the median is simply the middle value.
We can find the middle value by counting $(13 + 1) / 2 = 7$ .
The 7th value in our ordered list is 4, so the median is $4$ .

STEP 5

The range is the difference between the largest and smallest values.
Our largest value is $9$ and our smallest is $1$ .
So, the range is $9 - 1 = 8$ .

STEP 6

To find the interquartile range, we first need the first quartile (Q1) and the third quartile (Q3).
Q1 is the median of the lower half of the data, and Q3 is the median of the upper half.

STEP 7

Since our dataset has $13$ values, the median, which is $4$ , is the 7th value.
The lower half of the data consists of the first six values: $1, 2, 3, 3, 4, 4$ .
Since there are an even number of values, the median is the average of the middle two: $(3 + 3) / 2 = 3$ .
So, Q1 is $3$ .

STEP 8

The upper half of the data consists of the values after the median: $4, 4, 5, 5, 6, 7, 9$ .
Again, there are an odd number of values, so the median is the middle value, which is $5$ .
So, Q3 is $5$ .

STEP 9

The interquartile range (IQR) is the difference between Q3 and Q1: $\text{IQR} = Q3 - Q1 = 5 - 3 = 2$ .

STEP 10

a. Median: $4$ b. Range: $8$ c. Interquartile Range: $2$

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionEach dot in the following dot plot represents the number of chocolate chips in a single cookie in that box. a. Find the median of the data set:Answer: Blank 1 b. Find the range of the data set:Answer: Blank 2 c. Find the interquartile range:Answer: Blank 3

Studdy Solution

STEP 1

STEP 2

1. Arrange the Data2. Find the Median3. Find the Range4. Find the Quartiles5. Calculate the Interquartile Range

STEP 3

Let's **write out** all the chip counts, remembering each dot is a cookie!We have: 1,2,3,3,4,4,4,4,5,5,6,7,91, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 7, 91,2,3,3,4,4,4,4,5,5,6,7,9.There are **13** data points in total.

STEP 4

Since we have an **odd number** of data points (131313), the median is simply the middle value.We can find the middle value by counting (13+1)/2=7 (13 + 1) / 2 = 7 (13+1)/2=7.The **7th value** in our ordered list is **4**, so the median is 444.

STEP 5

The range is the difference between the **largest** and **smallest** values.Our largest value is 999 and our smallest is 111.So, the range is 9−1=8 9 - 1 = 8 9−1=8.

STEP 6

To find the interquartile range, we first need the **first quartile (Q1)** and the **third quartile (Q3)**.Q1 is the median of the lower half of the data, and Q3 is the median of the upper half.

STEP 7

STEP 8

The upper half of the data consists of the values after the median: 4,4,5,5,6,7,94, 4, 5, 5, 6, 7, 94,4,5,5,6,7,9.Again, there are an **odd number** of values, so the median is the middle value, which is 555.So, Q3 is 555.

STEP 9

The interquartile range (IQR) is the difference between Q3 and Q1: IQR=Q3−Q1=5−3=2 \text{IQR} = Q3 - Q1 = 5 - 3 = 2 IQR=Q3−Q1=5−3=2.

STEP 10

a. Median: 444 b. Range: 888 c. Interquartile Range: 222

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionEach dot in the following dot plot represents the number of chocolate chips in a single cookie in that box. a. Find the median of the data set:
Answer: Blank 1 b. Find the range of the data set:
Answer: Blank 2 c. Find the interquartile range:
Answer: Blank 3

1. Arrange the Data
2. Find the Median
3. Find the Range
4. Find the Quartiles
5. Calculate the Interquartile Range

Let's write out all the chip counts, remembering each dot is a cookie!
We have: $1, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 7, 9$ .
There are 13 data points in total.

Since we have an odd number of data points ( $13$ ), the median is simply the middle value.
We can find the middle value by counting $(13 + 1) / 2 = 7$ .
The 7th value in our ordered list is 4, so the median is $4$ .

The range is the difference between the largest and smallest values.
Our largest value is $9$ and our smallest is $1$ .
So, the range is $9 - 1 = 8$ .

To find the interquartile range, we first need the first quartile (Q1) and the third quartile (Q3).
Q1 is the median of the lower half of the data, and Q3 is the median of the upper half.

The upper half of the data consists of the values after the median: $4, 4, 5, 5, 6, 7, 9$ .
Again, there are an odd number of values, so the median is the middle value, which is $5$ .
So, Q3 is $5$ .

The interquartile range (IQR) is the difference between Q3 and Q1: $\text{IQR} = Q3 - Q1 = 5 - 3 = 2$ .

a. Median: $4$ b. Range: $8$ c. Interquartile Range: $2$