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Math  /  Data & Statistics

QuestionHere is a data set summarized as a stem-and-leaf plot:  4# 123346785#00013555666777777 6# 03778 7# 268\begin{array}{l|l} \text { 4\# } & 12334678 \\ 5 \# & 00013555666777777 \\ \text { 6\# } & 03778 \\ \text { 7\# } & 268 \end{array}
How many data values are in this data set? n=n= □\square What is the minimum value in the last class? ans == □\square What is the frequency of the modal class? (Hint, the modal class is the one with the most observations in it. How many observations are in that class?) frequency == □\square How many of the original values are greater than 60 ? ans == □\square

Studdy Solution

STEP 1

1. The stem-and-leaf plot provides a visual representation of the data set, where each "stem" represents a leading digit and each "leaf" represents a trailing digit.
2. Each leaf represents a single data value.
3. The minimum value in the last class can be determined from the leaves associated with the highest stem.
4. The modal class is identified by the stem with the highest number of leaves.
5. To find how many values are greater than a certain number, we consider the relevant stems and leaves.

STEP 2

1. Count the total number of data values.
2. Determine the minimum value in the last class.
3. Identify the frequency of the modal class.
4. Count the number of values greater than 60.

STEP 3

Count the total number of data values in the stem-and-leaf plot.
For each stem, count the number of leaves:
4#12334678⇒8 values5#00013555666777777⇒17 values6#03778⇒5 values7#268⇒3 values\begin{array}{l|l} \text{4\#} & 12334678 & \Rightarrow 8 \text{ values} \\ \text{5\#} & 00013555666777777 & \Rightarrow 17 \text{ values} \\ \text{6\#} & 03778 & \Rightarrow 5 \text{ values} \\ \text{7\#} & 268 & \Rightarrow 3 \text{ values} \end{array}
Total number of values:
8+17+5+3=338 + 17 + 5 + 3 = 33

STEP 4

Determine the minimum value in the last class. The last class has a stem of 7.
The leaves for the stem 7 are 2, 6, and 8. The minimum value in this class is:
7272

STEP 5

Identify the frequency of the modal class. The modal class is the one with the most observations.
The stem with the most leaves is 5, with 17 leaves. Thus, the frequency of the modal class is:
1717

STEP 6

Count the number of values greater than 60. This includes all values with stems of 6 and 7.
From the stem-and-leaf plot: - Stem 6 has 5 values. - Stem 7 has 3 values.
Total values greater than 60:
5+3=85 + 3 = 8
Total number of data values: n=33Minimum value in the last class: ans=72Frequency of the modal class: frequency=17Number of values greater than 60: ans=8\begin{array}{l} \text{Total number of data values: } n = 33 \\ \text{Minimum value in the last class: } \text{ans} = 72 \\ \text{Frequency of the modal class: } \text{frequency} = 17 \\ \text{Number of values greater than 60: } \text{ans} = 8 \end{array}

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