The Mobile Plan Flyer
A flyer from a mobile company says: 'Switch and save 40%! Our $25 plan gives 8 GB of data. Their $42 plan gives 20 GB. That's 40% cheaper.' It prints a bar chart with a vertical axis that starts at $20, so the $25 bar looks about one-quarter the height of the $42 bar. In small print, the $25 plan says 'unlimited social media' but speeds drop to 128 kbps after 2 GB of social media use; social media data does not count toward the 8 GB cap. The $42 plan includes 20 GB of full-speed data. A student uses about 15 GB of data each month, including 4 GB on social media. Extra data on the $25 plan costs $5 per GB; the $42 plan has no extra-data charge until 20 GB. Both prices include taxes.
1. Explain two ways the flyer's '40% cheaper' claim and chart could mislead a reader.
Read the worked answer
The 40% figure is calculated on the total price: ($42 − $25) ÷ $42 = 0.4048, about 40%. That is true only for the monthly bill, not for the amount of data. Per GB, the $25 plan costs $25 ÷ 8 = $3.13, while the $42 plan costs $42 ÷ 20 = $2.10; the $42 plan is about 33% cheaper per GB. The chart is also misleading because the vertical axis starts at $20. The visible bar heights are $5 and $22, so the $25 bar looks about 4.4 times smaller, although the real ratio is 25:42, or about 1:1.68. The word 'unlimited' is qualified by the 128 kbps throttle after 2 GB.
2. Calculate the monthly cost for this student on each plan for 15 GB of use. Which plan is cheaper for this student?
Read the worked answer
The student uses 15 GB total, of which 4 GB is social media. On the $25 plan, social media is included on top of the 8 GB but is slowed after 2 GB. Non-social data = 15 − 4 = 11 GB. The plan includes 8 GB, so extra non-social data = 3 GB. Extra cost = 3 × $5 = $15. Total = $25 + $15 = $40.
On the $42 plan, 15 GB is within the 20 GB allowance, so total = $42.
The $25 plan is cheaper by $2 for this usage, but 2 GB of the social media will be at slow speed.
3. The student often streams 6 GB of video on social media. How does that change the comparison?
Read the worked answer
If the student needs 6 GB of social media video at full speed, the $25 plan is a poor fit: only 2 GB is at full speed and the rest is throttled to 128 kbps, which is not practical for video. The $42 plan gives 20 GB of full-speed data and can cover 6 GB social plus 9 GB other without extra charge. The $2 monthly saving on the $25 plan is not worth losing 4 GB of usable video speed, so the $42 plan is the better choice for that user.