Name Date: Lesson 2-7: Histograms Learning Goals: #6: What is a histogram? How do we use frequency tables to construct histograms? Warm-Up: 1. Classify the following variables as qualitative or quantitative and also as discrete or continuous. a. The number of pages in a daily newspaper b. The maximum daily temperature in the city over 30 days c. The manufacturer of your cell-phone d. The number of goals shot by a soccer player 2. Calculate the 5 number summary of the following data # of Pets Frequency 0 4 1 6 2 3 3 1 4 2 Histogram- this is a bar graph of quantitative data used to show the trend of the variable being studied. What can you interpret from a histogram? What are the important aspects of a histogram? What is necessary when creating a histogram?
Let s take a look at one! Interpret the following histogram. The histogram shows the amount of money spent on food each week by a number of families. The amounts have been rounded to the nearest 10 dollars. a. How many families have been included in the histogram? b. What is the amount of money that most families spend? c. What percentage of families spent less than $170 each week? Steps for finding these statistics given a histogram: d. What is the mean amount of money spent on food by families each week? e. What is the standard deviation of our data? Let s use our Shoe Size Data to make a Histogram! Shoe Size Frequency 5 2 6 2 7 1 8 3 9 4 10 3 11 4 12 2 13 1 14 1
Practice 1. A random sample of people were asked How many times did you eat at a restaurant last week? A column graph was used to display the results. a) How many people were surveyed? b) Find the mode of the data. c) How many people surveyed did not eat at a restaurant at all last week? d) What percentage of people surveyed ate at a restaurant more than three times last week? 2. Arthur catches the train to school from a busy train station. Over the course of 30 days he counts the number of people waiting at the station when the train arrives. 17 25 32 19 45 40 22 15 38 8 21 29 37 25 42 35 19 31 26 7 22 11 27 44 24 22 32 18 40 29 a. Construct a tally and frequency table for this data using class intervals 0-9, 10-19, 40-49. Class Intervals Tally Frequency b. On how many days were there less than 10 people at the station? c. On what percentage of days were there at least 30 people at the station? d. Find the modal class of the data.
3. The figure below shows the lengths in centimeters of fish found in the net of a small trawler. a. Find the total number of fish in the net. 11 10 9 8 b. Find the modal length interval 7 Number of 6 fish 5 4 3 c. Find the interval containing the median length; 2 1 d. Find an estimate of the mean length. 1 0 10 **HINT** Make sure to translate the info in the histogram to a frequency chart first! 20 30 40 50 60 70 80 90 110 120130 Length (cm) Length Frequency e. Write down an estimate for the standard deviation of the lengths. 4. The bar chart below shows the number of people in a selection of families. a. How many families are represented? 10 8 b. Write down the mode of the distribution. Number of families 6 4 2 0 3 4 5 6 7 8 9 10 Number of people in a family c. Find, correct to the nearest whole number, the mean number of people in a family.
Name Date Lesson 2-7: Homework 1. The results of a Geography test for 25 students are given in the diagram. a. Write down the modal class. b. Calculate an estimate of the mean grade. 2. A safari park is open to visitors every day of the year. The numbers of cars that pass through the park each day for a whole year were recorded and are shown in the table. a. Calculate the median and Interquartile range of the data. b. Estimate the mean number of cars that traveled through the park. c. State an estimated standard deviation.
5. IB QUESTION: A random sample of 167 people who own mobile phones was used to collect data on the amount of time they spent per day using their phones. The results are displayed in the table below. Time spent per day (t minutes) 0 t 15 15 t 30 30 t 45 45 t 60 60 t 75 75 t 90 Number of people 21 32 35 41 27 11 a. On graph paper, draw a fully labeled histogram to represent the data. b. Calculate and interpret an estimate for the mean time people spend on their phones each day. c. What is the modal class?