Solved on Mar 25, 2024

Identify outliers among the 11 sandwich calorie values: $593, 594, 595, 596, 599, 602, 604, 604, 605, 606, 607$ .

STEP 1

1. To identify outliers, we will use the interquartile range (IQR) method.
2. The IQR is calculated as $IQR = Q3 - Q1$ , where $Q1$ is the first quartile (25th percentile) and $Q3$ is the third quartile (75th percentile).
3. Outliers are defined as observations that fall below $Q1 - 1.5 \times IQR$ or above $Q3 + 1.5 \times IQR$ .

STEP 2

1. Arrange the data in ascending order.
2. Calculate the first quartile ( $Q1$ ) and third quartile ( $Q3$ ).
3. Calculate the interquartile range ( $IQR$ ).
4. Determine the lower and upper bounds for outliers.
5. Identify any values that are outliers.

STEP 3

Arrange the data in ascending order.
The data is already given in ascending order: $593, 594, 595, 596, 599, 602, 604, 604, 605, 606, 607$

STEP 4

Calculate the first quartile ( $Q1$ ). Since we have 11 data points, $Q1$ is the value at the 3rd position (25% of 11 is approximately 2.75, so we round up to the 3rd data point).
$Q1 = 595$

STEP 5

Calculate the third quartile ( $Q3$ ). Since we have 11 data points, $Q3$ is the value at the 9th position (75% of 11 is approximately 8.25, so we round up to the 9th data point).
$Q3 = 605$

STEP 6

Calculate the interquartile range ( $IQR$ ).
$IQR = Q3 - Q1 = 605 - 595 = 10$

STEP 7

Determine the lower bound for outliers.
$\text{Lower Bound} = Q1 - 1.5 \times IQR = 595 - 1.5 \times 10 = 595 - 15 = 580$

STEP 8

Determine the upper bound for outliers.
$\text{Upper Bound} = Q3 + 1.5 \times IQR = 605 + 1.5 \times 10 = 605 + 15 = 620$

STEP 9

Identify any values that are outliers. We look for any data points below the lower bound or above the upper bound.
In our data set: $593, 594, 595, 596, 599, 602, 604, 604, 605, 606, 607$ None of the values are below 580 or above 620. Therefore, there are no outliers.
The solution is: None

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Identify outliers among the 11 sandwich calorie values: $593, 594, 595, 596, 599, 602, 604, 604, 605, 606, 607$ .

STEP 1

STEP 2

1. Arrange the data in ascending order.
2. Calculate the first quartile ( $Q1$ ) and third quartile ( $Q3$ ).
3. Calculate the interquartile range ( $IQR$ ).
4. Determine the lower and upper bounds for outliers.
5. Identify any values that are outliers.

STEP 3

Arrange the data in ascending order.
The data is already given in ascending order: $593, 594, 595, 596, 599, 602, 604, 604, 605, 606, 607$

STEP 4

Calculate the first quartile ( $Q1$ ). Since we have 11 data points, $Q1$ is the value at the 3rd position (25% of 11 is approximately 2.75, so we round up to the 3rd data point).
$Q1 = 595$

STEP 5

Calculate the third quartile ( $Q3$ ). Since we have 11 data points, $Q3$ is the value at the 9th position (75% of 11 is approximately 8.25, so we round up to the 9th data point).
$Q3 = 605$

STEP 6

Calculate the interquartile range ( $IQR$ ).
$IQR = Q3 - Q1 = 605 - 595 = 10$

STEP 7

Determine the lower bound for outliers.
$\text{Lower Bound} = Q1 - 1.5 \times IQR = 595 - 1.5 \times 10 = 595 - 15 = 580$

STEP 8

Determine the upper bound for outliers.
$\text{Upper Bound} = Q3 + 1.5 \times IQR = 605 + 1.5 \times 10 = 605 + 15 = 620$

STEP 9

Identify any values that are outliers. We look for any data points below the lower bound or above the upper bound.
In our data set: $593, 594, 595, 596, 599, 602, 604, 604, 605, 606, 607$ None of the values are below 580 or above 620. Therefore, there are no outliers.
The solution is: None

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Identify outliers among the 11 sandwich calorie values: 593,594,595,596,599,602,604,604,605,606,607593, 594, 595, 596, 599, 602, 604, 604, 605, 606, 607593,594,595,596,599,602,604,604,605,606,607.

STEP 1

STEP 2

1. Arrange the data in ascending order.2. Calculate the first quartile (Q1Q1Q1) and third quartile (Q3Q3Q3).3. Calculate the interquartile range (IQRIQRIQR).4. Determine the lower and upper bounds for outliers.5. Identify any values that are outliers.

STEP 3

Arrange the data in ascending order.The data is already given in ascending order: 593,594,595,596,599,602,604,604,605,606,607 593, 594, 595, 596, 599, 602, 604, 604, 605, 606, 607 593,594,595,596,599,602,604,604,605,606,607

STEP 4

Calculate the first quartile (Q1Q1Q1). Since we have 11 data points, Q1Q1Q1 is the value at the 3rd position (25% of 11 is approximately 2.75, so we round up to the 3rd data point).Q1=595 Q1 = 595 Q1=595

STEP 5

Calculate the third quartile (Q3Q3Q3). Since we have 11 data points, Q3Q3Q3 is the value at the 9th position (75% of 11 is approximately 8.25, so we round up to the 9th data point).Q3=605 Q3 = 605 Q3=605

STEP 6

Calculate the interquartile range (IQRIQRIQR).IQR=Q3−Q1=605−595=10 IQR = Q3 - Q1 = 605 - 595 = 10 IQR=Q3−Q1=605−595=10

STEP 7

Determine the lower bound for outliers.Lower Bound=Q1−1.5×IQR=595−1.5×10=595−15=580 \text{Lower Bound} = Q1 - 1.5 \times IQR = 595 - 1.5 \times 10 = 595 - 15 = 580 Lower Bound=Q1−1.5×IQR=595−1.5×10=595−15=580

STEP 8

Determine the upper bound for outliers.Upper Bound=Q3+1.5×IQR=605+1.5×10=605+15=620 \text{Upper Bound} = Q3 + 1.5 \times IQR = 605 + 1.5 \times 10 = 605 + 15 = 620 Upper Bound=Q3+1.5×IQR=605+1.5×10=605+15=620

STEP 9

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Identify outliers among the 11 sandwich calorie values: $593, 594, 595, 596, 599, 602, 604, 604, 605, 606, 607$ .

1. Arrange the data in ascending order.
2. Calculate the first quartile ( $Q1$ ) and third quartile ( $Q3$ ).
3. Calculate the interquartile range ( $IQR$ ).
4. Determine the lower and upper bounds for outliers.
5. Identify any values that are outliers.

Arrange the data in ascending order.
The data is already given in ascending order: $593, 594, 595, 596, 599, 602, 604, 604, 605, 606, 607$

Calculate the first quartile ( $Q1$ ). Since we have 11 data points, $Q1$ is the value at the 3rd position (25% of 11 is approximately 2.75, so we round up to the 3rd data point).
$Q1 = 595$

Calculate the third quartile ( $Q3$ ). Since we have 11 data points, $Q3$ is the value at the 9th position (75% of 11 is approximately 8.25, so we round up to the 9th data point).
$Q3 = 605$

Calculate the interquartile range ( $IQR$ ).
$IQR = Q3 - Q1 = 605 - 595 = 10$

Determine the lower bound for outliers.
$\text{Lower Bound} = Q1 - 1.5 \times IQR = 595 - 1.5 \times 10 = 595 - 15 = 580$

Determine the upper bound for outliers.
$\text{Upper Bound} = Q3 + 1.5 \times IQR = 605 + 1.5 \times 10 = 605 + 15 = 620$