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name: _______________ time (min): block: ___ unit 12 data representatio…

Question

name: _____________ time (min): block: _
unit 12 data representations practice
use the box plot (and 5 - number summary)
box plot with number line: 11,13,15,17,19,21,23,25
min=?
q1: ?
median: ?
q3: ?
max: ?
a large school system summarizes the number of teachers at 50 schools in the area.
table with school data: minimum: 10 teachers, q1: 40, median: 85 teachers, q3: 95, maximum: 130

  1. create a box plot that shows this information.

number line: 0,20,40,60,80,100,120, label: teachers per school

  1. create a histogram that shows this information.

histogram axes: 0-120, teachers per school

  1. which of these data displays most easily shows how many schools have at least 100 teachers per school? explain your reasoning.

Explanation:

Response
First Box - and - Whisker Plot (Top)
Step 1: Identify Minimum (Min)

The minimum value in a box - and - whisker plot is the left - most dot on the whisker. From the plot, the left - most dot is at 12. So, Min = 12.

Step 2: Identify First Quartile (Q1)

The first quartile (Q1) is the left - hand edge of the box. Looking at the box, the left edge is at 15. So, Q1 = 15.

Step 3: Identify Median

The median is the line inside the box. The line inside the box is at 19. So, Median = 19.

Step 4: Identify Third Quartile (Q3)

The third quartile (Q3) is the right - hand edge of the box. The right edge of the box is at 22. So, Q3 = 22.

Step 5: Identify Maximum (Max)

The maximum value is the right - most dot on the whisker. The right - most dot is at 25. So, Max = 25.

1. Box - and - Whisker Plot for Teachers per School

To create a box - and - whisker plot, we use the given values: Minimum = 10, Q1 = 40, Median = 65, Q2 = 95 (wait, actually Q3 should be 95? Maybe a typo, probably Q3 = 95), Maximum = 130.

  • Draw a number line from 0 to 130 with appropriate intervals (20, 40, 60, 80, 100, 120 as given).
  • Plot the minimum (10) as the left - most dot on the whisker.
  • The left edge of the box (Q1) is at 40.
  • The line inside the box (Median) is at 65.
  • The right edge of the box (Q3) is at 95.
  • The right - most dot on the whisker (Maximum) is at 130. Then connect the box to the whiskers.
2. Histogram for Teachers per School

First, we need to organize the data from the frequency table (the left - hand table with "10 - 29", "30 - 49", etc. and frequencies). Let's assume the intervals are: 0 - 19, 20 - 39, 40 - 59, 60 - 79, 80 - 99, 100 - 119, 120 - 139 (or based on the given "10 Teachers", "40", "65", "95", "130" which might imply intervals around these values). But from the frequency table (the left table with rows like "10 - 29" with frequency 10, "30 - 49" with frequency 9, etc.):

  • For the interval 10 - 29 (or 0 - 29), the frequency is 10.
  • For 30 - 49, frequency is 9.
  • For 50 - 69, frequency is 16.
  • For 70 - 89, frequency is 8.
  • For 90 - 109, frequency is 6.
  • For 110 - 129, frequency is 6.
  • For 130 - 149, frequency is 1.
  • For 150 - 169, frequency is 4.
  • For 170 - 189, frequency is 13. (Wait, the table is a bit unclear, but we'll proceed with the general method)

To draw the histogram:

  • The x - axis is "teachers per school" with intervals (e.g., 10 - 29, 30 - 49, etc.).
  • The y - axis is "frequency" (number of schools).
  • For each interval, draw a bar with height equal to the frequency of that interval. For example, for the interval 10 - 29, the bar height is 10, for 30 - 49 it's 9, etc.
3. Data Display for "At Least 100 Teachers"

To determine which data display (box - and - whisker plot, histogram, or the frequency table) shows how many schools have at least 100 teachers:

  • Histogram: We can sum the frequencies of the intervals that represent 100 or more teachers (e.g., 100 - 109, 110 - 119, 120 - 129, 130 - 139, etc.). By looking at the heights of the bars for these intervals and adding them up, we can find the number of schools with at least 100 teachers.
  • Box - and - Whisker Plot: It shows quartiles and extremes but not the frequency of individual intervals. It can tell us the range of values but not how many data points are in a specific range (like ≥100) directly.
  • Frequency Table: We can sum the frequencies of the rows that correspond to 100 or more teachers.

The histogram most easily shows how many schools have at least 100 teachers because we can visually identify the ba…

Answer:

s for the First Box - and - Whisker Plot:
Min: \(\boldsymbol{12}\)

Q1: \(\boldsymbol{15}\)

Median: \(\boldsymbol{19}\)

Q3: \(\boldsymbol{22}\)

Max: \(\boldsymbol{25}\)

(For the other parts, the box - and - whisker plot is drawn as described, the histogram is drawn with bars for each interval with height equal to frequency, and the histogram (or frequency table) is the best display for "at least 100 teachers" as explained)