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Lessons:
- 7th grade
- S3.B2.k6ab, Lesson 2, Handout,
Independent Practice, Q2.
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Tutorials:
- 4th grade
- S3.B2.K2a, Tutorial 2,
Age Appropriate Skill Application.
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No
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- 10th grade
- S4.B2.A1c, Tutorial 1,
Check Your Learning.
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The
interquartile range (IQR) is the difference between the upper (or 3rd)
quartile value and the lower (or 1st) quartile value. To determine the lower
quartile, rank the terms from low to high and determine the median of the
lower half of the terms. In this case, the 13 terms from low to high are .3,
.8, .9, .9, 1.1, 1.1, 1.8, 1.8, 2.0, 2.0, 2.1, 3.5, and 7.4. Since we have 13
terms, the median is the middle term: 1.8. (This is also known as the 2nd
quartile value.) With this as the dividing point, the lower half consists of
six values: 3, .8, .9, .9, 1.1, and 1.1. Since we have six terms, the median
is the mean of the 3rd and 4th terms. Mean (often called average) is equal to
sum divided by the number of terms. 9 + 1.1 divided by 2 is 1.0. Therefore,
1.0 is the lower quartile value.
The upper quartile value is the median of the upper half of the terms. The
upper half of all the data consists of these six values: 1.8, 2.0, 2.0, 2.1,
3.5, and 7.4. The median of this half is the mean of its 3rd and 4th terms.
2.0 + 2.1 divided by 2 equals 2.05. Therefore, 2.05 is the upper quartile
value.
Since the interquartile range is the difference between the upper and lower
quartile values, the interquartile range is 2.05 - 1, which equals 1.05. |
The
interquartile range (IQR) is the difference between the upper (or 3rd)
quartile value and the lower (or 1st) quartile value. To determine the lower
quartile, rank the terms from low to high and determine the median of the
lower half of the terms. In this case, the 13 terms from low to high are .3,
.8, .9, .9, 1.1, 1.1, 1.2, 1.8,
2.0, 2.0, 2.1, 3.5, and 7.4. Since we have 13 terms, the median is the middle
term: 1.2. (This is also known as
the 2nd quartile value.) With this as the dividing point, the lower half
consists of six values: 3, .8, .9, .9, 1.1, and 1.1. Since we have six terms,
the median is the mean of the 3rd and 4th terms. Mean (often called average)
is equal to sum divided by the number of terms. .9 + .9 divided by 2 is .9.
Therefore, .9 is the lower
quartile value.
The upper quartile value is the median of the upper half of the terms. The
upper half of all the data consists of these six values: 1.8, 2.0, 2.0, 2.1,
3.5, and 7.4. The median of this half is the mean of its 3rd and 4th terms.
2.0 + 2.1 divided by 2 equals 2.05. Therefore, 2.05 is the upper quartile
value.
Since the interquartile range is the difference between the upper and lower
quartile values, the interquartile range is 2.05 - .9, which equals 1.15. |
- S4.B2.a1d, Tutorial 2,
Practice 2.
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Why
is Option B correct?
The range for week 1 is 57 - 49, which is 8. We can´t say for sure what the
range is for week 2, but it is reasonable to say that the data indicates a
downward trend from day to day. The range for week 2, based on the existing
data is 37 - 29, which is 8. If the trend continues, the range will be
greater than 8. |
Correct!
The interquartile range for week 1 is 5 (56 - 51). We can not say for sure
what the range is for week 2, but the trend is downward, so it is likely that
the number of purchases on Friday will be less than 29. Therefore, the
interquartile range will be 4 (33 - 29). The interquartile range for week 2
is less than the interquartile range for week 1. |
- S4.B2.a1f, Tutorial 1,
Practice 2.
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Why
is option A correct? The data for The News at Night, when arranged from least
to greatest looks like this (all data in millions).
3,
3, 3, 3, 4, 4, 5, 5, 6, 6, 6, 6 7, 8, 8, 9
The
median divides these 16 numbers into two groups of 8. The lower quartile is the mean of the 4th and 5th terms, which are 3 and 4. Therefore the lower quartile is 3.5. The upper quartile is the mean of the 12th and 13th terms, which are 6 and 7. Therefore
the upper quartile is 6.5. The
interquartile range is the upper quartile minus the lower quartile: 6.5 - 3.5 = 3.
The
data for AM News, when arranged from least to greatest looks like this (all
data in millions).
4,
4, 5, 5, 5, 5, 6, 6, 6, 7, 8, 8, 8, 10, 10, 11
The
median divides these 16 numbers into two groups of 8. The lower quartile is the mean of the 4th and 5th terms, which are both 5. Therefore the lower quartile is 5. The upper quartile is the mean of the 12th and 13th terms, which are both 8. Therefore the
upper quartile is 8. The interquartile
range is the upper quartile minus the lower quartile: 8 - 5 = 3.
Since
the interquartile ranges are both 3, their difference is 0. |
Why
is option A correct? The data for The
News at Night, when arranged from least to greatest looks like this (all
data in millions).
4, 4, 5, 5, 5, 5, 6, 6, 6, 7, 8, 8, 8,
10, 10, 11
The median divides these 16 numbers into two groups of 8. The lower quartile
is the mean of the 4th and 5th terms, which are both 5.
Therefore the lower quartile is 5. The upper quartile is the mean of the 12th and 13th terms, which are both 8. Therefore the upper quartile is
8. The interquartile range is the upper quartile minus the lower quartile: 8  5  3.
The data for AM News, when
arranged from least to greatest looks like this (all data in millions).
3, 3, 3, 3, 4, 4, 5, 5, 6, 6, 6, 6 7,
8, 8, 9
The median divides these 16 numbers into two groups of 8. The lower quartile
is the mean of the 4th and 5th terms, which are 3 and
4. Therefore the lower quartile is 3.5. The upper quartile is the mean of the
12th and 13th terms, which are 6 and 7. Therefore the
upper quartile is 6.5. The interquartile range is the upper quartile minus
the lower quartile: 6.5 - 3.5 = 3.
Since the interquartile ranges are both 3, their difference is 0. |
- S4.B2.a1g, Tutorial 1,
Check Your Learning.
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The
interquartile range is the length of the interval between the upper quartile
value, Q1, and the lower quartile value, Q3. In short,
Interquartile range = Q3 - Q1 |
The
interquartile range is the length of the interval between the lower quartile value, Q1, and the upper quartile value, Q3. In short,
Interquartile range = Q3 - Q1 |
- S4.B2.a1h, Tutorial 1,
Check Your Learning.
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C. 15 - 17
Why is option C correct? The median is the middle
item in a set when all the age groups are arranged from least to greatest.
Since we have 185 members, the median is the 91st item.
The 91st item in the set would be 15 - 17. |
C. 15 - 17
Why is option C correct? The median is the middle
item in a set when all the age groups are arranged from least to greatest.
Since we have 185 members, the median is the 93rd item.
The 93rd item in the
set would be 15 - 17.
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